Optimal Stochastic Control Schemes within a Structural Reliability Framework (SpringerBriefs in Statistics)

The Book Addresses The Topic Of On-line Implementation Of Structural And Mechanical Design Criteria As An Explicit Part Of Optimal Control Schemes. The Intention Of The Present Research Monograph Is To Reflect Recent Developments Within This Area. Examples Of Application Of Relevant Control Algorithms Are Included To Illustrate Their Practical Implementation. These Examples Are Mainly Taken From The Area Of Marine Technology With The Multi-component External Loading Being Represented As Both Varying In Time And With Magnitudes That Are Represented As Statistical Quantities. The Relevant Target Group Will Be Mechanical And Structural Engineers That Are Concerned With “smart Components And Structures” Where Optimal Design Principles And Control Actuators Are Combined. The Book Is Also Relevant For Engineers E.g. Involved In Mechatronics And Control Applications. 1.introduction -- 2.structural Limit States And Reliability Measures -- 3.dynamic Structural Response Analysis And Probabilistic Representation -- 4.categories Of On-line Control Schemes Based On Structural Reliability Criteria -- 5. Example Applications Related To On-line Control Schemes -- 6. Conclusions. By Bernt J. Leira. Contents 5 1 Introduction 7 References 8 2 Structural Limit States and Reliability Measures 9 Abstract 9 2.1...Introduction 9 2.2...Failure Function and Probability of Failure 10 2.3...Time-Varying Load and Capacity 13 2.4...Simplified Calculation of Failure Probability for Gaussian Random Variables 15 2.5...Calculation of Failure Probability for Non-Gaussian Random Variables 16 References 18 3 Dynamic Structural Response Analysis and Probabilistic Representation 19 Abstract 19 3.1...General 19 3.2...Environmental Modeling 20 3.3...Dynamic Response Analysis 22 3.4...Response Statistics for Scalar Gaussian Processes 23 3.5...Reliability Formulations for Scalar Gaussian Processes 28 3.6...Multi-Dimensional Response Statistics 30 3.6.1 Introduction 30 3.6.2 Outcrossing-Rate Analysis 31 3.6.3 Local Maxima and Extremes 32 3.6.4 Fatigue Analysis for Multi-Dimensional Processes 36 References 38 4 Categories of On-Line Control Schemes Based on Structural Reliability Criteria 40 Abstract 40 4.1...General 40 4.2...Control Schemes Involving Structural Reliability Criteria 41 4.2.1 Introduction 41 4.2.2 Various Types of Simplified Structural Reliability Indices 41 4.2.3 Simplistic Illustrative Example and Comparison of Reliability Indices 45 4.2.4 Off-Line Control Schemes 47 4.2.5 Control Scheme Based on Reliability Monitoring 48 4.2.6 On-Line Control Schemes 49 4.3...Off-Line ‘‘Calibration’’ of LQG Schemes 51 4.3.1 General 51 4.3.2 LQG Control of Stationary Quasi-Static Response 51 4.3.3 Alternative Loss Function Based on Structural Failure Cost 53 4.3.4 The Case with Two-Scale Response Characteristics 57 4.3.5 Application to Simplified Example 59 4.4...Concluding Remarks 60 References 61 5 Example Applications Related to On-line Control Schemes 62 Abstract 62 5.1...General 62 5.2...Vessel Dynamics 63 5.2.1 Vessel Motion 63 5.2.2 PID Control Algorithm for Dynamic Positioning 65 5.3...Example of Control Scheme Based on Structural Reliability Monitoring 66 5.3.1 General 66 5.3.2 System Model and Behavior Without Position Control 66 5.3.3 System Model and Behavior with Position Control Implemented 69 5.4...Control Schemes Based on On-Line Computation of Reliability Measures 75 5.4.1 Example 1 75 5.4.2 Example 2: Position Mooring of Floating Vessel Based on Reliability Index Criteria 92 5.4.3 Further Examples of Application 96 5.5...Concluding Remarks 98 References 99 6 Conclusions 101 Front Matter....Pages i-vi Introduction....Pages 1-2 Structural Limit States and Reliability Measures....Pages 3-12 Dynamic Structural Response Analysis and Probabilistic Representation....Pages 13-33 Categories of On-Line Control Schemes Based on Structural Reliability Criteria....Pages 35-56 Example Applications Related to On-Line Control Schemes....Pages 57-95 Conclusions....Pages 97-98