Industrial Application of Fuzzy Logic Control Tutorial and

Industrial Application of Fuzzy Logic Control Tutorial and Workshop © Constantin von Altrock Fuzzy Logic Development Methodology According to ISO/IEC Standards Inform Software Corporation 2001 Midwest Rd. Oak Brook, IL 60521, U. S. A. X Relevant Standards for Fuzzy Logic X Future Standards for Fuzzy Logic X General Development Methodology - Goals - Phase Plan - Support with Fuzzy Software Tools X Specific Development Methodology - Goals - Design Decisions - Fuzzy Design Wizards German Version Available! Phone 630 -268 -7550 Fax 630 -268 -7554 Email: fuzzy@informusa. com Internet: www. fuzzytech. com © INFORM 1990 -1998 Slide 1

Fuzzy Logic: - Relevant Standards ISO 9000 International Quality Standard X Design Documentation X Design Modifications Documentation X Testing Procedure Documentation IEC 1131+ Industrial Automation Standard X Data Exchange Formats for Portability Both General and Specific Standards for Fuzzy Logic Systems Development Exist ! © INFORM 1990 -1998 X Integration with Conventional Techniques X Development Methodology Slide 2

Fuzzy Logic: - Future Standards IEEE Standard Specific Standards for Fuzzy Logic: X Terminology and Algorithms (Different words for the same things and same words for different things are confusing for practitioners) X Universal Programming Language for Fuzzy Logic X Meaningful Benchmarks (Real-world oriented benchmarks for platform selection and comparison) X Further Refined Development Methodology X Fuzzy-”Plug-Ins” for Standard Applications Under Construction ! © INFORM 1990 -1998 X Adaptation Techniques for Fuzzy Logic Systems Slide 3

General Fuzzy Logic Development Methodology Goals of the General Fuzzy Logic Development Methodology: X Definition of Non-Ambiguous and Transparent Design Steps X Definition of Minimum Criteria for Project Structuring, Reporting, and Documentation (Final System, Revision, and Design Steps) Validation Complies with ISO 9000 ! The Results of This Are: X A Complete and Transparent Coverage of the Entire Development Process X Raised Awareness for Design Step Decision Criteria and Their Consequences X Non-Ambiguous Mapping of External Services in a Complete Development Project X Protection from Liability Claims X Unfortunately, Also More Effort… © INFORM 1990 -1998 Slide 4

General Fuzzy Logic Development Methodology Phase Plan: The General Fuzzy Logic Development Methodology Structures the Complete Project ! Preliminary Evaluation A-Audit Prototype B-Audit Off-Line Optimization Setup Optimization Documentation A-Report B-Report Project Start Acceptance Audit = Capture of Process Knowledge and Experience from Operators and Engineers Report = Protocol of an Audit Result © INFORM 1990 -1998 Slide 5

General Fuzzy Logic Development Methodology Preliminary Evaluation Assessment As to Whether Fuzzy Logic Is Applicable for the Given Application Problem Analysis Before Project Start ! Evaluation Criteria: X Has Fuzzy Logic Been Previously Applied to a Similar Application With Success? X Is It a Multi-Variable Type Control Problem? X Do Operators and Engineers Possess Knowledge About Any Relevant Interdependencies of the Process Variables? X Can Further Knowledge About the Process Behavior Be Gained By Observation Or Experiments? X Is It Difficult to Obtain a Mathematical Model from the Process? © INFORM 1990 -1998 Slide 6

General Fuzzy Logic Development Methodology A-Audit Systematic Representation of the Available Process Knowledge ! Preparation: X Auditors: Familiarization with the Domain of the Application, Definition of a Specific Questionnaire X Plant Operators: Documentation of the Existing Measurement and Control Systems, Description of All Relevant Sensors and Actuators of the Process -- Including Min/Max Values and Tolerances, and Provision of Trend Charts Which Display Typical Behavior Action: X Analysis of the Quality Variables and Criteria Variables X Analysis of the Command Variables X Analysis of the Current Performance A-Report: X Written Summary of the Audit by the Auditors, Review and Acceptance by the Plant Operator © INFORM 1990 -1998 Slide 7

General Fuzzy Logic Development Methodology Prototype Implementation of a Prototype Based on the A-Report: X As a Demonstration for the B-Audit X As a Starting Point for the Next Development Step Prototype Generation According to the Specific Fuzzy Development Methodology: X Definition of the System Structure X Creation of the Vocabulary X Formulation of a First Rule Base Rapid Application Development ! © INFORM 1990 -1998 Slide 8

General Fuzzy Logic Development Methodology B-Audit Revision of the Prototype ! Preparation: X Auditors: Preparation of the Prototype as a Demonstration, Creation of a Questionnaire Comprising All Open Issues Action: X Joint Discussions About Inconsistencies and Missing Parts of the A-Audit , Plus Further In-Depth Discussion about all Unclear Issues Still Remaining X Revision of the A-Report to the B-Report X Definition of Procedures for a Safe Setup of the Controller with Respect to not Disturbing the Running Process and Endangering Process Safety B-Report: X Written Summary of the Audit by the Auditors, Plus Review and Acceptance by the Plant Operator © INFORM 1990 -1998 Slide 9

General Fuzzy Logic Development Methodology Off-Line Optimization Extension and Refinement of the Prototype Based on the Results of the B-Report: X Revision of the Linguistic Variable Definitions X Revision and Extension of the Rule Base Verification By: X Off-Line Analysis of the Partial Transfer Characteristics X Use of Existing Software Simulations of the Plant X Use of Existing Recorded Process Data for Testing Implementation of Operation Knowledge ! © INFORM 1990 -1998 Slide 10

General Fuzzy Logic Development Methodology Setup Online Optimization Setup of the Fuzzy Logic Controller: X Implementation on the Target Hardware and Online-Link to the Development PC X Integration with Existing Control System and Implementation of Pre-/Postprocessing X Creation of Safety Function (Limits, Manual Operation Switch, Safe State, . . ) Online Optimization of the Fuzzy Logic Controller: X “Open-Loop” Operation to Validate the Controller’s Behavior X “Supervised” Operation for Fine-Tuning of Rules and Membership Functions X “What-If” Analyses to Optimize Control Performance Verification with the Running Process ! © INFORM 1990 -1998 Slide 11

General Fuzzy Logic Development Methodology Documentation of the Final Design of the Fuzzy Logic Controller: X Structure of Fuzzy Logic System X Vocabulary of Fuzzy Logic System X Rule Bases of Fuzzy Logic System Using Fuzzy Logic Development Tools Drastically Reduces Paperwork Expenditures ! Documentation of the Development Process: X Audit Reports X Final Reports X Development History of the Fuzzy Logic System © INFORM 1990 -1998 Slide 12

General Fuzzy Logic Development Methodology fuzzy. TECH Software Development Tools for Fuzzy Logic Systems Support the Process By: X Including Local Documentation for All Objects of a Fuzzy Logic System X Automatic Generation of Complete System and History Documentation X An Embedded Revision Control System The Inter-Operation of these Components Reduces the Documentation Effort by 75 - 95% ! © INFORM 1990 -1998 Slide 13

General Fuzzy Logic Development Methodology Ability to Include Comments About Any Object of a Design Within the Development Software: Definition of Comments: Transparent View of the Comments During Development: The Documentation Evolves DURING Development ! © INFORM 1990 -1998 Slide 14

General Fuzzy Logic Development Methodology Automated Generation of Complete System Documentation: X Export, Modify, and Print in Word Processor X Automatic Integration into Plant Operation Manual X Documentation in Multiple Languages Complete Documentation at Any Level of Development in Just Seconds ! © INFORM 1990 -1998 Slide 15

General Fuzzy Logic Development Methodology Integrated Revision Control System: X Complete Development History in a Single File X Documentation of all Levels of Development X Protection Against Unauthorized Access the Entire Development History at Any Time ! © INFORM 1990 -1998 Slide 16

Specific Fuzzy Logic Development Methodology Goals of the Specific Fuzzy Logic Development Methodology: X Definition of a Clear and Non-Ambiguous Design Approach to all Components and Objects of a Fuzzy Logic System (Linguistic Variables, Rules, Structure, …) X Definition of the Involved Criteria for the Design Decisions Validation Complies with ISO 9000 ! The Results of This Are: X “Cookbook-Recipe”-Type Definition with Respect to Real-World Needs X Shorter Initial Training Period for Fuzzy Logic Designers X Avoidance of Misunderstandings and Errors X Protection Against Unsound Liability Claims X Future Expansion or Modification of the System Without Risks © INFORM 1990 -1998 Slide 17

Specific Fuzzy Logic Development Methodology Design Steps: Design Methods Design Decisions: X Structural Analysis X Expert Audit X Structural Definition X Definition of Vocabulary X Definition of Inter-Dependencies X Verification ? X Offline Simulation X Offline Plausibility Testing of the Rule Blocks X Offline Test Using Process Data ? X Online Optimization X Type of Membership Function X Inference Methods X Operator Choice X Choice of Defuzzification Method The Specific Fuzzy Logic Development Methodology Structures the Actual Fuzzy System Design ! © INFORM 1990 -1998 Slide 18

Design Step Overview Structure Linguistic Variables X The Individual Design Decisions Are Defined by Their Design Criteria and Consequences for the Final System Behavior X Each Design Step Involves Its Individual Methodology and Design Decisions Fuzzy Rules X “Sanity-Checks” Are Conducted After Each Step Offline Test X Compliance with the Procedures Can Be Checked (It Is “Certifiable”) Setup Maintenance © INFORM 1990 -1998 X The Development Path of a Fuzzy Logic System Developed Is Transparent and Reproducible, Even to Others Well-Defined Design Approach Rather Than “Trial-and-Error” ! Slide 19

Definition of Systems Structure Output Variables Linguistic Variables Input Variables Fuzzy Rules Connections Offline Test Defuzzification Setup Maintenance © INFORM 1990 -1998 X Output Variables: What Types of Decisions Must the Fuzzy Logic System Make (0/1, inc/dec, absolute)? X Input Variables: Which Are Available from the Process, and Which Shall Be Used First? X Connections: Which Input Variables Influence What Output Variables? Are Intermediate Aggregations Possible? X Defuzzification: “Best Compromise” or “Most Plausible Solution”? The First Development Step Defines the Outline of the Fuzzy Logic System ! Slide 20

Systems Structure - Output Variables What Types of Decisions Shall the Fuzzy Logic System Make: X Absolute Values to Actuators Input Variables Connections X Absolute Values As Set Points to Underlying Controllers X Relative Values to Modify the Set Point Value of Underlying Controllers (increment/decrement) X Discrete Decisions (on/off, . . . ) Defuzzification Documentation of the Output Variables: X What Is the Influence of Each Output Variable in the Process? X What Is the Interval in which the Output Variable Shall Be Varied, and Which “Typical” Values Exist? Exact Definition of the Expected Outputs ! © INFORM 1990 -1998 X Are There “Safe State” Values? Slide 21

Systems Structure - Input Variables Output Variables Input Variables Connections Defuzzification Documentation of All Available Input Variables: X Which Aspect of the Process Are Described by the Input Variable? X What Is the Value Interval of the Input Variable? Which “Typical” Values Exist? X What Are the Tolerances of the Sensors, and How Accurate Is the Measured Information? X What Is the Time Delay of the Input Variable? Which of the Available Input Variables Shall Be Used: Inventory of All Available Input Variables! © INFORM 1990 -1998 X For Each Output Variable, Define a List of the Its Influencing Input Variables, Sorted by Relative Importance X From This List, Identify the Smallest Set of Input Variables That Suffice to Control All Output Variables Slide 22

Systems Structure - Connections Output Variables Input Variables Connections Identification of Interdependencies in the Decision Structure: X For Each Output Variable, Which Input Variables Are Influencing It? X Can Meaningful Intermediate Variables that Describe Process States Be Defined? Defuzzification Simple Structure = Complex Rule Definitions The More a Decision Can Be Structured, the More Transparent the Resulting System Will Be ! © INFORM 1990 -1998 Complex Structure = Simple Rule Definitions Slide 23

Systems Structure - Defuzzification Output Variables Input Variables Connections Defuzzification The Use of the Output Variable in the Control System Determines the Defuzzification Method ! © INFORM 1990 -1998 Definition of the Defuzzification Method for Each Output Variable: X For Continuous Variables: “Best Compromise“ : = Co. M X For Discrete Variables: “Most Plausible Result” : = Mo. M #1: IF Temp = high OR Press = high THEN CH 4 = low #2: IF Temp = med AND Press = med THEN CH 4 = med v_high med low 1 µ (0. 6) (0. 2) Co. M #1 #2 0 #1: IF Temp = high AND Flow = ok THEN Fire = on #2: IF Temp = med AND Flow = low THEN Fire = off 1 #2 on µ off 0 CH 4 (0. 8) (0. 9) #1 Mo. M Fire Slide 24

Definition of System Structure Output Variables The Fuzzy Design Wizard in fuzzy. TECH: Input Variables Connections Defuzzification Embedded “Fuzzy-Expert”! © INFORM 1990 -1998 Slide 25

Definition of Linguistic Variables X How Many Terms Should Be Defined for Each Linguistic Variable? Structure Linguistic Variables Number of Terms Fuzzy Rules X Which Type of Membership Functions Should Be Used for the Variables? X How Can Plausible Membership Functions for the Terms Be Defined? Type of Memb. Fct. Offline Test Membership Fct. Setup Maintenance © INFORM 1990 -1998 The Second Design Step Defines the Vocabulary of the Fuzzy Logic System ! Slide 26

Linguistic Variables - Number of Terms Heuristic Method (“Cookbook Recipe”): X Nearly All Linguistic Variables Have Between 3 and 7 Terms Type of Memb. Fct. X Most Often, the Number of Terms Is an Odd Number X. . . Hence the Number of Terms Is Either 3, 5, or 7 Membership Fct. Practical Approach: X Initial “Test”-Rules Indicate the Number of Terms Necessary X A Rule-of-Thumb: Start With 3 Terms for Each Input Variable and 5 Terms for Each Output Variable Start With A Minimum Number of Terms, Since New Terms Can Be Added As Needed ! © INFORM 1990 -1998 Slide 27

Linguistic Variables - Membership Function Types Number of Terms Type of Memb. Fct. Membership Fct. Empirical Psycho Linguistic Research Has Shown that Membership Function Definitions Should Obey the Following Axioms: 1. µ(x) continuous over X 2. µ‘(x) continuous over X 3. µ‘‘(x) continuous over X 4. µ: minµ{maxx{µ‘‘(x)}} for all X Cubic Interpolative Spline Functions Satisfy These Axioms: For Most Real-World Applications, a Linear Approximation Suffices ! © INFORM 1990 -1998 Slide 28

Linguistic Variables - Membership Functions Number of Terms Definition in Four Easy Steps: 1. For Each Term, Define a Typical Value/Interval Type of Memb. Fct. Membership Fct. 2. Define µ=1 for This Value/Interval 3. Define µ=0 from Which the Next Neighbor is µ=1 4. Join Points With Linear / Cubic Spline Functions Example of Linguistic Variable “Error”: ONE Typical Value Per Linguistic Term Suffices for Definition of Membership Functions ! © INFORM 1990 -1998 large_p: 10 positive: 3 zero: 0 negative: -3 large_n: -10 1 µ 0 -10 -5 0 Error +5 +10 Slide 29

Linguistic Variables - Membership Functions Number of Terms Definition in Four Easy Steps: 1. For Each Term, Define a Typical Value/Interval Type of Memb. Fct. 2. Define µ=1 for This Value/Interval 3. Define µ=0 from Which the Next Neighbor is µ=1 Membership Fct. 4. Join Points With Linear / Cubic Spline Functions Example of Linguistic Variable “Error”: A “Typical Value” May Also Be an Interval ! large_p: 10 positive: 3 zero: [-1; 1] negative: -3 large_n: -10 1 µ 0 -10 © INFORM 1990 -1998 -5 0 Error +5 +10 Slide 30

Linguistic Variables - Membership Functions Number of Terms Structured Definition of Linguistic Variables in fuzzy. TECH: Type of Memb. Fct. Membership Fct. Definition of Complete Sets of Membership Functions in One Easy Step ! © INFORM 1990 -1998 Slide 31

Definition of the Fuzzy Rules Base Structure X Which Fuzzy Logic Operator for the Rule Premise Aggregation Step? Linguistic Variables X Which Fuzzy Logic Operator for the Rule Result Aggregation Step? X How Are the Actual Fuzzy Logic Rules Defined? Fuzzy Rules Aggregation Op. Offline Test Result Agg. Op. Setup Definition of Rules Maintenance © INFORM 1990 -1998 The Third Design Step Defines the Actual Control Strategy ! Slide 32

Definition of the Fuzzy Rules - Aggregation Operator Aggregation Op. Elementary Fuzzy Logic Operators: Result Agg. Op. X AND: µAv. B = min{ µA; µB } X OR: µA+B = max{ µA; µB } X NOT: µ-A = 1 - µA Definition of Rules . . . Model Human Evaluation and Reasoning Poorly Sometimes Example: IF Car=fast AND Car=economical THEN Car=good X Car 1: X Car 2: X Car 3: The Exclusive Use of Elementary Fuzzy Logic Operators Can Inflate the Rule Base ! © INFORM 1990 -1998 180 km/h: µ=0. 3 9 l/100 km: µ=0. 4 -> 0. 3 180 km/h: µ=0. 3 7 l/100 km: µ=0. 6 -> 0. 3 175 km/h: µ=0. 25 4 l/100 km: µ=0. 9 -> 0. 25 Mock-Up Solution: Define More Fuzzy Rules: pretty_fast highly_economic pretty_good IF Car=fast AND Car=economical THEN Car=good somewhat_fast mildly_economic just_ok Slide 33

Definition of the Fuzzy Rules - Aggregation Operator Aggregation Op. Transfer Characeristics of MIN and MAX: Result Agg. Op. Definition of Rules Compensatory Operators Better Represent Human Evaluation and Reasoning: MIN AND In Most Real-World Applications, MIN and MAX Are Sufficient ! © INFORM 1990 -1998 MAX OR The Gamma-Operator Can Be Tuned: Slide 34

Definition of the Fuzzy Rules - Aggregation Operator Aggregation Op. fuzzy. TECH Uses Parametric Fuzzy Operators: Result Agg. Op. Definition of Rules Transparent Parameterization Through Instant Visualization of Transfer Characteristics ! © INFORM 1990 -1998 Slide 35

Definition of the Fuzzy Rules - Result Agg. Operator Aggregation Op. Two Methods Are Applied in Real-World Applications: X “The Winner Takes It All” (MAX) Result Agg. Op. Definition of Rules X “One Man, One Vote” (BSUM) Rules: MAX: BSUM: med (0. 6) med (1. 0) #1: . . . => Power = high (0. 3) #2: . . . => Power = med (0. 1) #3: . . . => Power = med (0. 4) #4: . . . => Power = med (0. 6) #5: . . . => Power = low (0. 0) If the Rule Base Is Not Symmetrical, BSUM Can Yield Wrong Results ! © INFORM 1990 -1998 Slide 36

Definition of the Fuzzy Rules - Definition of Rules Aggregation Op. Basic Properties of Rule Bases: X Normalization (all Brackets Resolved) Result Agg. Op. X Elementation (only “AND” Operators Used) Example of a Non-Normalized Non-Elementary Rule: Definition of Rules IF (((Press_1 = low AND Press_2 = low) OR (Press_3 = med AND NOT Temp_2 = high)) AND (Press_1 = low OR Temp_1 = high)) THEN CH 4 = med Different Rule Block Definition Approaches: X Induction: Define the “THEN”-Part for All Possible Input Term Combinations (only with 2. . 3 Input Variable per Rule Block) The Experience to Be Implemented Determines the Procedure! © INFORM 1990 -1998 X Deduction: Define Rules As Single Pieces of Experience (Prefer “Thin” Rules) X Linear Approach: Stepwise Optimization of a “Linear” Fuzzy Rule Base (Mostly Used with “Direct” Fuzzy Controllers) Slide 37

Definition of the Fuzzy Rules - Definition of Rules Aggregation Op. fuzzy. TECH Supports All Three Approaches: X Automatic Generation of Inductive Fuzzy Rule Bases Result Agg. Op. Definition of Rules Definition of a Consequence for Every Possible Situation ! © INFORM 1990 -1998 Slide 38

Definition of the Fuzzy Rules - Definition of Rules Aggregation Op. Result Agg. Op. fuzzy. TECH Supports All Three Approaches: X Optimized Editors and Analyzers for Deductive Rule Definition (Table, Text, and Matrix Type Representation) Definition of Rules Each Rule Expresses an Aspect of the Experience ! © INFORM 1990 -1998 Slide 39

Definition of the Fuzzy Rules - Definition of Rules Aggregation Op. fuzzy. TECH Supports All Three Approaches: X Fuzzy Rule Wizard for Automated Generation of Linear Rule Blocks Result Agg. Op. Definition of Rules Complete Rule Block Definition in One Step ! © INFORM 1990 -1998 Slide 40

Off-Line Testing Structure Rule Validation Linguistic Variables Process Simulation Fuzzy Rules X Which Fuzzy Rules Are Missing, Superfluous, or Conflicting? X Fine-Tuning the Linguistic Variables With the Help of Process Simulation X Optimization With Data From the Actual Process Data Test Off-Line Testing Setup Maintenance © INFORM 1990 -1998 In Off-Line Testing, the First Verification of the Fuzzy System Occurs ! Slide 41

Off-Line Testing - Rule Validation 1 Rule Validation Analysis Tools in fuzzy. TECH for Rule Validation: Process Simulation Process Data Test Direct Analysis of the Data Range in a 3 D Graph ! © INFORM 1990 -1998 Slide 42

Off-Line Testing - Rule Validation 2 Rule Validation Analysis Tools in fuzzy. TECH for Rule Validation: Process Simulation Process Data Test Verification of Individual Rule Blocks With the Statistics Analyzer ! © INFORM 1990 -1998 Slide 43

Off-Line Testing - Process Simulation 1 Rule Validation Dynamic Links in fuzzy. TECH to Simulation Tools and Programming Languages: Process Data Test X Fuzzy Control Blocks in Vis. Sim™, Matlab/SIMULINK™, . . . X Standard Links Like DDE, DLL, OLE, Active. X, Data, . . . X You Can Tie in the Editors and Analyzers of fuzzy. TECH With Your Own Software X Process Simulation Either Complete fuzzy. TECH (With All Editors and Analyzers) or Runtime Module (Highest Performance) Can Be Used Open Links Allow Connection With Most Any Software ! © INFORM 1990 -1998 Slide 44

Off-Line Testing - Process Simulation 2 Rule Validation Dynamic Monitoring and Tuning in fuzzy. TECH: Process Simulation Process Data Test Asynchronous Coupling of Simulation and fuzzy. TECH ! © INFORM 1990 -1998 Slide 45

Off-Line Testing - Process Data Test Rule Validation Dynamic Optimization Using Actual Process Data in fuzzy. TECH: Process Simulation Process Data Test Verification of the Entire Fuzzy Controller in Real Process Situations ! © INFORM 1990 -1998 Slide 46

Setup Structure X Implementation of the Fuzzy Controller on the Target Hardware Linguistic Variables X Implementation of the Online Process Link Implementation Fuzzy Rules Warm Operation Offline Test Hot Operation Setup Maintenance © INFORM 1990 -1998 X Warm Operation = Output of the Fuzzy Controller Is Not Switched Through to the Process X Hot Operation = Output of the Fuzzy System Is Switched Through to the Process Final Validation of the Complete Fuzzy System in Online Operation ! Slide 47

Setup - Implementation on Target Various Implementation Techniques Available in fuzzy. TECH: X X Embedded Control: Assembly Code Kernels Industrial Automation: Fuzzy Function Blocks for PLCs Process Supervisory Control: Fuzzy Modules for DCS, SCADA. . Universal: Common Source Code Output (C, C++, VB, Pascal, . . ) Online Link Between the Process Hardware (Target) and fuzzy. TECH: For Most Industrial Target Platforms, an Optimized Implementation Technique Exists ! © INFORM 1990 -1998 Slide 48

Setup: Warm/Hot Operation Analysis of Behavior Over Time in fuzzy. TECH: X Dynamic in All Editors and Analyzers X Special Behavior Over Time of Variables, Terms and Rules in a Time Plot Real-Time Remote Debugging for Systems Verification ! © INFORM 1990 -1998 Slide 49

Operation and Maintenance X Final Documentation of the Fuzzy Logic Design and Its Integration (Comprises All Previous Design Steps Documentation) Structure Linguistic Variables X Configuration of the Monitor Component for the Supervision of Fuzzy Logic System Performance Fuzzy Rules Documentation Offline Test X Optional Review of Fuzzy Logic Design and Modifications of the System As Result of Review Monitoring Setup Review Maintenance © INFORM 1990 -1998 Development Methodology Continues During Operation ! Slide 50

Operation and Maintenance fuzzy. TECH Supports These Steps Through: X Documentation: Documentation Generator and Revision Control System X Remote Tracing for Online Monitoring Unsupervised Monitoring Using Trigger Conditions ! X Review of the Linguistic Variables and Fuzzy Rules Through “What-If” Analyses © INFORM 1990 -1998 Slide 51

Summary of Specific Fuzzy Development Methodology 1. 2. 3. 4. 5. 6. Structure Definition 1. 1 Documentation of All Output Variables 1. 2 Documentation of All Input Variables 1. 3 Structuring of the Decision (“many small rule blocks”) 1. 4 Defuzzification Method Selection (“Best Compromise“ or “Most Plausible Solution”? ) Linguistic Variables 2. 1 Number of Terms per Variable (start with 3 per input and 5 per output variable) 2. 2 Type of Membership Function (start with Standard-MBFs) 2. 3 Membership Function Definition by Standard Method (typical values => MBF’s) Fuzzy Rule Definition 3. 1 Fuzzy Operator for Aggregation (start with MIN) 3. 2 Fuzzy Operator for Result Aggregation (start with MAX) 3. 3 Select Rule Definition Approach Depending on Application (Inductive, Deductive, Linear) Offline Testing 4. 1 Validation of the Rule Blocks (identification of missing and conflicting rules) 4. 2 Testing Using Process Simulation (if available) 4. 3 Testing Using Real Process Data (if available) An Easily Reproduced, Certifiable Setup Process to Reach Your Solution ! Operation and Maintenance © INFORM 1990 -1998 Slide 52

fuzzy. TECH Supports Entire Fuzzy Design Methodology Structure Linguistic Variables => Fuzzy Design Wizard The Optimal Tool for Every Step of the Design Process ! => Linguistic Variable Wizard Fuzzy Rules => Fuzzy Rule Wizard, Rule Block Utilities Offline Test => Offline Debug Mode, Analyzer Setup => Online Debug Mode, Analyzer Maintenance © INFORM 1990 -1998 => Trace, Documentation Generator, Revision Control System Slide 53

Further Reading / Literature “Hands-On” Guides for Fuzzy Logic Systems Development: "Fuzzy Logic and Neuro. Fuzzy Applications Explained" by Constantin von Altrock, $39. 95, Prentice Hall, ISBN 0 -1336 -8465 -2, shows how to design technical fuzzy logic applications and contains a demo of the fuzzy. TECH software with 10 control system simulations to experiment with. It also explains the use of fuzzy and Neuro. Fuzzy techniques in over 70 case studies. "[This book]. . . is packed with information which is presented in a reader-friendly fashion. It is a must for anyone who is interested in the analysis and design of fuzzy logic based systems. ” Lotfi Zadeh, Berkeley "Fuzzy Logic and Neuro. Fuzzy Applications in Business and Finance" by Constantin von Altrock, $39. 95, Prentice Hall 1996, ISBN 0 -13 -591512 -0, shows how to design business and finance fuzzy logic applications and contains a demo of the fuzzy. TECH for Business software with numerous case studies to experiment with. It also explains the use of fuzzy and Neuro. Fuzzy techniques in recent successful practical implementations. ". . . We owe to Constantin v. Altrock our thanks and congratulations for authoring an innovative text that is leading the way. Fuzzy Logic and Neuro. Fuzzy in Business and Finance is must reading for anyone who has a serious interest in adding new tools to the armamentarium of decision analysis. . . " Lotfi Zadeh, Berkeley © INFORM 1990 -1998 Slide 54