Sensitivity Analysis for Fuzzy- Sensitivity Analysis for Fuzzy- Logic-Based Life-Cycle Analysis Logic-Based Life-Cycle Analysis Approach Approach Chen Chen Chen and Gerardo W. Flintsch Chen and Gerardo W. Flintsch Roadway Infrastructure Group, VTTI Roadway Infrastructure Group, VTTI The Via Department of Civil and Environmental Engineering The Via Department of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Virginia Polytechnic Institute and State University
Soft Computing based LCCA Tools Soft Computing based LCCA Tools Introduction Introduction 1. 1. Engineering Economic Analysis Engineering Economic Analysis 2. 2. Soft Computing Applications for Soft Computing Applications for 3. 3. Life- -Cycle Cost Analysis Cycle Cost Analysis Life Fuzzy Logic based LCCA Algorithm Fuzzy Logic based LCCA Algorithm 4. 4. Sensitivity Analysis Sensitivity Analysis 5. 5. Summaries and Conclusions Summaries and Conclusions 6. 6.
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. Business-like Engineering Objectives Integration ~ Asset Management Primer. FHWA, 1999 ~ Asset Management for the Roads Sector. OECD, 2001
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 21 st Century
2. Engineering Economic Analysis 2. Engineering Economic Analysis Life- -cycle cost analysis cycle cost analysis Life � � Developing alternatives to accomplish the 1. objectives of a project Determining the schedule of initial and future 2. activities necessary for each alternative, Estimating the costs associated with these activities 3. (or expenditure streams), Discounting and adding these costs to compute the 4. total life-cycle costs, and Evaluating the results 5. ~ 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 � ⎡ ⎤ 1 n ∑ ⎢ ⎥ LCC InitialCos t FutureCost = + × ( 1 ) n ⎣ ⎦ i + 1 � Probabilistic Methods Probabilistic Methods � � Probability distribution function (PDF) � Simulation ( e.g. Monte Carlo simulation) � Risk analysis
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
Engineering Engineering Delay Delay Engineering Engineering Delay Delay Construction Pavement Costs Alternatives Construction Construction Traffic Control Traffic Control Construction Construction Traffic Control Traffic Control Year = 1 Year = Year + 1 Pavement Pavement Pavement Pavement Deteriorated Deteriorated Configuration Configuration Configuration Configuration Pavement Conditions Pavement Conditions Traffic Traffic Structural Condition Structural Condition Traffic Traffic Structural Condition Structural Condition Updated Conditions Updated Conditions Functional Condition Functional Condition Year Year Functional Condition Functional Condition Structural Condition Structural Condition Year Year Structural Condition Structural Condition User Costs Functional Condition Functional Condition Functional Condition Functional Condition Year = Year + 1 MR & R No Yes Rule-Based (FL) MR & R Life Cycle Costs Costs
Deterioration Model Deterioration Model Year Year Structure Structure Year Year Structure Structure Traffic Traffic … … Traffic Traffic … … PSI PSI Time Gap Time Gap PSI PSI Time Gap Time Gap Year = Year + 1 Year = Year + 1 PCI PCI … … PCI PCI … … Fuzzy Policy Fuzzy Trigger Model Model ∆ PSI ∆ PSI Time Gap = 0 Time Gap = 0 ∆ PSI ∆ PSI Time Gap = 0 Time Gap = 0 MR & R No Yes Action ∆ PCI ∆ PCI … … ∆ PCI ∆ PCI … … Life Cycle Co$t MR & R Scenario
Fuzzy Logic System Structure Fuzzy Logic System Structure Rules Output Crisp Crisp y x Fuzzifier Outputs Inputs Processor Fuzzy Fuzzy Inference Outputs Inputs y = f (x)
Traditional Membership Functions Traditional Membership Functions Very Low Medium Very High High Low 1 Membership Function 0 0 0.2 0.4 0.6 0.8 1 Priority
Example Membership Functions Example Membership Functions Very Low Medium High Very High Low 1 Membership Function 0 0 0.2 0.4 0.6 0.8 1 Priority
EXAMPLE FUZZY RULES (Do- -Nothing) Nothing) EXAMPLE FUZZY RULES (Do � IF IF PSI PSI is is excellent , THEN the Priority Priority of Do of Do- -Nothing Nothing excellent , THEN the � is very high ; is very high ; � IF IF PCI PCI is is excellent , THEN the Priority Priority of Do of Do- -Nothing Nothing excellent , THEN the � is very high ; is very high ; � IF IF Time Gap Time Gap is is very short , THEN the Priority Priority of Do of Do- - very short , THEN the � Nothing is very high ; Nothing is very high ; � …. …. �
5. Sensitivity Analysis
Research Taskes Taskes Research 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 1 Lane # 1 Direction # 5280 Length (ft) 12 Width (ft) 7040 Area (SY) SN = 5.0 M R = 7,500 psi
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