Sensitivity Analysis for Fuzzy- Sensitivity Analysis for Fuzzy- - - PowerPoint PPT Presentation

Roadway Infrastructure Group, VTTI The Via Department of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Roadway Infrastructure Group, VTTI The Via Department of Civil and Environmental Engineering Virginia Polytechnic Institute and State University

Sensitivity Analysis for Fuzzy- Logic-Based Life-Cycle Analysis Approach Sensitivity Analysis for Fuzzy- Logic-Based Life-Cycle Analysis Approach

Chen Chen Chen Chen and and Gerardo W. Flintsch Gerardo W. Flintsch

Soft Computing based LCCA Tools Soft Computing based LCCA Tools

1. 1.

Introduction Introduction

2. 2.

Engineering Economic Analysis Engineering Economic Analysis

3. 3.

Soft Computing Applications for Soft Computing Applications for Life Life-

• Cycle Cost Analysis

Cycle Cost Analysis

4. 4.

Fuzzy Logic based LCCA Algorithm Fuzzy Logic based LCCA Algorithm

5. 5.

Sensitivity Analysis Sensitivity Analysis

6. 6.

Summaries and Conclusions Summaries and Conclusions

• 1. Introduction

• 1. Introduction
• 1. Introduction
• Maintaining transportation infrastructure

Maintaining transportation infrastructure networks is more challenging than ever networks is more challenging than ever before… before…

Roads = D+, Bridges = C, Overall: D+ 1/3 of U.S. roads are in poor or mediocre condition; Road conditions contribute to as many as 13,800

highway fatalities annually

~ The 2001 Report Card for America’s Infrastructure. ASCE, 2003

• 1. Introduction
• 1. Introduction
• How to balance:

How to balance:

Growing M&R demands Aging infrastructure Constrained resources

• 1. Introduction
• 1. Introduction
• Asset Management serves as today’s best

Asset Management serves as today’s best approach for balancing them. approach for balancing them.

~ Asset Management Primer. FHWA, 1999 ~ Asset Management for the Roads Sector. OECD, 2001

Business-like Objectives

Engineering Integration

• 2. Engineering Economic

Analysis

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• Engineering economic analysis

Engineering economic analysis

Encompasses a collection of techniques that can be

used to select, evaluate, recommend, and prioritize investment options according to their level of economic efficiency.

Life-Cycle cost analysis Benefit cost analysis Risk analysis Impact analysis …

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• Life

Life-

• cycle cost analysis is

cycle cost analysis is “ “… …a process for a process for evaluating the total economic worth of a usable evaluating the total economic worth of a usable project segment by analyzing initial costs and project segment by analyzing initial costs and discounted future cost, such as maintenance, user, discounted future cost, such as maintenance, user, reconstruction, rehabilitation, restoring, and reconstruction, rehabilitation, restoring, and resurfacing costs, over the life of the project resurfacing costs, over the life of the project segment. segment.” ”

~Defined in Section 303, Quality Improvement, of the National Highway System NHS Designation Act of 1995 ~Modified by Transportation Equity Act for the 21st Century

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• Life

Life-

• cycle cost analysis

cycle cost analysis

1.

Developing alternatives to accomplish the

• bjectives of a project

2.

Determining the schedule of initial and future activities necessary for each alternative,

3.

Estimating the costs associated with these activities (or expenditure streams),

4.

Discounting and adding these costs to compute the total life-cycle costs, and

5.

Evaluating the results

~ Life-Cycle Cost Analysis in Pavement Design – Interim Technical Bulletin. FHWA, 1998

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• LCCA technical issues/ unanswered

LCCA technical issues/ unanswered questions: questions:

Discount rate Non-agency cost Data quality M&R costs and salvage value Modeling asset deterioration Analysis period …

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• Deterministic Methods

Deterministic Methods

• Probabilistic Methods

Probabilistic Methods

Probability distribution function (PDF) Simulation (e.g. Monte Carlo simulation) Risk analysis

∑

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + × + =

n n

i FutureCost t InitialCos LCC

1

) 1 ( 1

• 2. Engineering Economic Analysis
• 2. Engineering Economic Analysis
• The ability of evaluating the risk due to

The ability of evaluating the risk due to uncertainty give probabilistic approaches uncertainty give probabilistic approaches an advantage over deterministic methods an advantage over deterministic methods

• Is it enough?

Is it enough?

• UNCERTAINTY

UNCERTAINTY

Of an random nature Of an ambiguous nature ?

• 3. Soft Computing-based

Life-Cycle Cost Analysis

• 3. Soft Life Cycle Cost Analysis
• 3. Soft Life Cycle Cost Analysis
• Soft computing is an umbrella of computational

Soft computing is an umbrella of computational techniques that handles both subjective and techniques that handles both subjective and numerical information, and it also tolerates numerical information, and it also tolerates imprecision, uncertainty, and ambiguity imprecision, uncertainty, and ambiguity ~

~ Zadeh Zadeh, 1977 , 1977 Fuzzy logic systems Artificial neural networks Evolutionary computation Genetic algorithms, chaotic programming, etc. Hybrid systems

• 3. Soft Life Cycle Cost Analysis
• 3. Soft Life Cycle Cost Analysis
• Fuzzy Logic Systems

Fuzzy Logic Systems

Incorporate engineering expertise and prior

knowledge into the decision along life span

Efficiently handle subjective and uncertain

information that is hard to be processed in traditional way

Disadvantage: membership definition; rule

development; subjective bias of the system.

• 4. Fuzzy Logic-based

Life-Cycle Cost Analysis Algorithm

Pavement Alternatives Construction Costs

Year Year Traffic Traffic Pavement Configuration Pavement Configuration Year Year Traffic Traffic Pavement Configuration Pavement Configuration Deteriorated Pavement Conditions Structural Condition Structural Condition Functional Condition Functional Condition Deteriorated Pavement Conditions Structural Condition Structural Condition Functional Condition Functional Condition Engineering Engineering Construction Construction Delay Delay Traffic Control Traffic Control Engineering Engineering Construction Construction Delay Delay Traffic Control Traffic Control

No

Year = Year + 1 Updated Conditions Structural Condition Structural Condition Functional Condition Functional Condition Updated Conditions Structural Condition Structural Condition Functional Condition Functional Condition

Yes

Year = Year + 1

MR & R Costs Life Cycle Costs

MR & R

Rule-Based (FL)

User Costs

Year = 1

PSI PSI PCI PCI Time Gap Time Gap … … PSI PSI PCI PCI Time Gap Time Gap … …

Fuzzy Policy Model Fuzzy Trigger Model MR & R Action

Year Year Traffic Traffic Structure Structure … … Deterioration Model Year Year Traffic Traffic Structure Structure … … Deterioration Model ∆PSI ∆PSI ∆PCI ∆PCI Time Gap = 0 Time Gap = 0 … … ∆PSI ∆PSI ∆PCI ∆PCI Time Gap = 0 Time Gap = 0 … …

Yes

Life Cycle Co$t

Year = Year + 1 No Year = Year + 1

MR & R Scenario

Fuzzy Logic System Structure Fuzzy Logic System Structure

Fuzzifier Inference Output Processor Rules

Crisp Inputs Crisp Outputs Fuzzy Inputs Fuzzy Outputs

x y y = f (x)

Traditional Membership Functions Traditional Membership Functions

Very Low Low Medium High Very High 1 0.2 0.4 0.6 0.8 1 Priority Membership Function

Very Low Low Medium High Very High 1 0.2 0.4 0.6 0.8 1

Priority Membership Function

Example Membership Functions Example Membership Functions

EXAMPLE FUZZY RULES (Do EXAMPLE FUZZY RULES (Do-

• Nothing)

Nothing)

• IF

IF PSI PSI is is excellent excellent, THEN the , THEN the Priority Priority of Do

• f Do-
• Nothing

Nothing is is very high very high; ;

• IF

IF PCI PCI is is excellent excellent, THEN the , THEN the Priority Priority of Do

• f Do-
• Nothing

Nothing is is very high very high; ;

• IF

IF Time Gap Time Gap is is very short very short, THEN the , THEN the Priority Priority of Do

• f Do-
• Nothing is

Nothing is very high very high; ;

• ….

….

• 5. Sensitivity Analysis

Research Research Taskes Taskes

• Sensitivity analyses of inference rules

Sensitivity analyses of inference rules (SA1) (SA1)

• Sensitivity analyses of effective fuzzy

Sensitivity analyses of effective fuzzy areas (SA2) areas (SA2)

• Sensitivity analyses of overlapping of

Sensitivity analyses of overlapping of adjacent membership functions (SA3) adjacent membership functions (SA3)

Base Case Base Case

Pavement Configuration Pavement Configuration

MR = 7,500 psi SN = 5.0

Lane # 1 Direction # 1 Length (ft) 5280 Width (ft) 12 Area (SY) 7040

Traffic Assumption Traffic Assumption

Traffic: Based on the traffic volume monitored on Traffic: Based on the traffic volume monitored on I I-

• 81 between 1997 and 2002

81 between 1997 and 2002

200 400 600 800 1000 1200 1400 1600 1800 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Year ESAL (thousands)

200 400 600 800 1000 1200 1400 1600 1800 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Year ESAL (thousands)

ESAL(0) = 306,301 Growth Factor: 1.5%

Performance Model Performance Model

) 5 . 1 2 . 4 )( 10 (

] ) 1 /( 1094 4 . ][ 07 . 8 ) log( 32 . 2 20 . ) 1 log( 36 . 9 ) [log(

19 . 5

− = ∆

− + + − + + − − SN M SN S Z ESAL

R n

PSI

• Present Serviceability Index

Present Serviceability Index

• Pavement Condition Rating

Pavement Condition Rating

2

) ( 22 . 100 AGE PCI − =

~ Washington State PMS, 1990 ~ Washington State PMS, 1990 ~ Based on AASHTO Flexible Pavement Design Equation ~ Based on AASHTO Flexible Pavement Design Equation

Cost Assumption Cost Assumption

Cost: According to “Life Cycle Cost Analysis Cost: According to “Life Cycle Cost Analysis Pavement Options”, VTRC, 2002. Pavement Options”, VTRC, 2002.

Material Unit Price AC Surface 40.00 $ AC Base 31.00 $ CTA 21.00 $ Surface Treatment 1.50 $ Mill 0.50 $ Drainage Layer 25.00 $ Removing Existing 2.00 $

Effect of MR&R treatments Effect of MR&R treatments

min(PCI+20, 100) min(PCI+20, 100) min(PSI+0.5, 4.5) min(PSI+0.5, 4.5)

Preventive Preventive Maintenance Maintenance Back to 100 Back to 100 Back to 4.5 Back to 4.5 Reconstruction Reconstruction Back to 100 Back to 100 Back to 4.5 Back to 4.5 Thick Overlay Thick Overlay Back to 100 Back to 100 Back to 4.5 Back to 4.5 Medium Overlay Medium Overlay Back to 100 Back to 100 Back to 4.5 Back to 4.5 Thin Overlay Thin Overlay Time Gap Time Gap PCI PCI PSI PSI Treatment Effect Treatment Effect Treatment Treatment

0.00 0.20 0.40 0.60 0.80 1.00 10 20 30 40 50

Tim e (year) Priority Do Nothing Medium Overlay

Output Priorities Output Priorities

• 250
• 200
• 150
• 100
• 50

50 100 150 200 250 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Time (year) NPV $ (Thousands)

Expenditure Stream for Medium Expenditure Stream for Medium Overlay MR&R Policy Overlay MR&R Policy

Results for the Simplified Example Results for the Simplified Example

98.9 3.77 3.77 $ 233,720.44

Preventive Preventive Maintenance Maintenance

80.2 80.2 3.38 3.38 $ 358,110,28 $ 358,110,28

Reconstruction Reconstruction

85.6 85.6 4.13 4.13 $ 279,239.19 $ 279,239.19

Thick Overlay Thick Overlay

89.2 89.2 4.14 $ 263,609.52 $ 263,609.52

Medium Overlay Medium Overlay

93.3 93.3 4.05 4.05 $ 240,163.68 $ 240,163.68

Thin Overlay Thin Overlay Average PCI Average PCI Average PSI Average PSI Total Cost (NPV) Total Cost (NPV) Fuzzy Logic Based LCCA Result Fuzzy Logic Based LCCA Result Policy Policy

Sensitivity Analysis Sensitivity Analysis

SA1: Inference rules SA1: Inference rules

base case PSI PCI TimeGap PSI+PCI PSI+TimeGap PCI+TimeGap 200 250 300 350 400 450 500 $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

Finding of SA1 Finding of SA1

• In the seven rule group combinations,

In the seven rule group combinations, preventive maintenance policy is the preventive maintenance policy is the winning strategy in most cases. One winning strategy in most cases. One exception happened on model with PSI exception happened on model with PSI rules only, medium overlay is the rules only, medium overlay is the champion in that case. Thus the model is champion in that case. Thus the model is relative robust against changing the rules relative robust against changing the rules used. used.

SA2: Effective Fuzzy Area SA2: Effective Fuzzy Area

1 1 Priority Degree of Membership

SA2: Effective Fuzzy Area SA2: Effective Fuzzy Area

0.5 1 1.5 2 2.5 200 250 300 350 400 450 500 PSI EFA Lower Limit $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA2: Effective Fuzzy Area SA2: Effective Fuzzy Area

1 2 3 4 5 6 7 8 9 200 250 300 350 400 450 500 TimeGap EFA Lower Limit $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA2: Effective Fuzzy Area SA2: Effective Fuzzy Area

4 8 12 16 20 24 28 32 36 40 200 250 300 350 400 450 500 PCI EFA Lower Limit $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA2: Effective Fuzzy Area SA2: Effective Fuzzy Area

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 200 250 300 350 400 450 500 Priority EFA Lower Limit $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

Finding of SA2 Finding of SA2

• Lifecycle costs are sensitive to changes of PSI

Lifecycle costs are sensitive to changes of PSI and PCI (which are control variables) EFA and PCI (which are control variables) EFA position in their meaningful ranges. position in their meaningful ranges.

• Proper EFA position could be found by

Proper EFA position could be found by comparing model output with similar projects’ comparing model output with similar projects’ data or using engineering judgment of data or using engineering judgment of reasonable cost range. reasonable cost range.

• EFA positions of priority

EFA positions of priority-

• type output variables do

type output variables do not have significant effect on final lifecycle costs. not have significant effect on final lifecycle costs.

SA3: Overlapping of MF SA3: Overlapping of MF

1 1 Priority Degree of Membership

SA3: Overlapping of MF SA3: Overlapping of MF

1 2 3 4 5 6 7 8 9 10 200 250 300 350 400 450 500 PSI Step Number $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA3: Overlapping of MF SA3: Overlapping of MF

1 2 3 4 5 6 7 8 200 250 300 350 400 450 500 TimeGap Step Number $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA3: Overlapping of MF SA3: Overlapping of MF

1 2 3 4 5 6 7 8 9 10 200 250 300 350 400 450 500 PCI Step Number $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA3: Overlapping of MF SA3: Overlapping of MF

1 2 3 4 5 6 7 8 9 10 200 250 300 350 400 450 500 Priority Step Number $ thousands Preventive Maintenance Thin Overlay Medium Overlay Thick Overlay Reconstruction

SA3: Overlapping of MF SA3: Overlapping of MF

1 2 3 4 5 6 7 8 9 10 200 210 220 230 240 250 260 270 280 290 300 Step Number $ thousands EFA Lower Limit: 0 EFA Lower Limit: 0.1 EFA Lower Limit: 0.2 EFA Lower Limit: 0.3

SA3: Overlapping of MF SA3: Overlapping of MF

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.58 0.6 0.62 0.64 0.66 0.68 0.7 PSI Priority Overlapping step: 6 Overlapping step: 7 Overlapping step: 8 Overlapping step: 9

Finding of SA3 Finding of SA3

• The abnormal phenomenon of SA2 is what

The abnormal phenomenon of SA2 is what should be avoided in modeling lifecycle should be avoided in modeling lifecycle maintenance activities. This could be done by maintenance activities. This could be done by changing EFA locations to avoid inputs to fall in changing EFA locations to avoid inputs to fall in local crest or trough area on solution surface, or local crest or trough area on solution surface, or by increasing overlapping of adjacent by increasing overlapping of adjacent membership functions. Considering local crest membership functions. Considering local crest

• r trough areas are hard to be located at design
• r trough areas are hard to be located at design

phase, increasing overlapping is a more phase, increasing overlapping is a more practical way to avoid this kind of abnormal practical way to avoid this kind of abnormal phenomena. phenomena.

• 6. Summaries and Conclusions
• 6. Summaries and Conclusions
• It is feasible and practical to use fuzzy logic

It is feasible and practical to use fuzzy logic techniques in LCCA. techniques in LCCA.

• The linguistic inference rules could expedite

The linguistic inference rules could expedite incorporating engineering knowledge into the incorporating engineering knowledge into the estimation process of lifecycle costs. estimation process of lifecycle costs.

• The outputs of fuzzy

The outputs of fuzzy-

• logic

logic-

• based LCCA model

based LCCA model are sensitive to membership functions’ feature. are sensitive to membership functions’ feature.

• 6. Summaries and Conclusions
• 6. Summaries and Conclusions
• The location of control variable’s effective fuzzy

The location of control variable’s effective fuzzy area has an immediate effect on output lifecycle area has an immediate effect on output lifecycle costs. costs.

• The shape of membership functions does not

The shape of membership functions does not influence output much but a larger overlapping influence output much but a larger overlapping area of adjacent membership functions could area of adjacent membership functions could help avoid the abnormal occurrence of MR&R help avoid the abnormal occurrence of MR&R activities. activities.

• The effects of membership functions of output

The effects of membership functions of output variable are less than input variables. variable are less than input variables.

Acknowledgement Acknowledgement

• This project was partially funded by the National

This project was partially funded by the National Science Foundation grant CMS # 0236694. Science Foundation grant CMS # 0236694.