Probabilistic finite element model updating using Bayesian statistics : applications to aeronautical and mechanical engineering /: applications to aeronautical and mechanical engineering. (2017)

• Record Type: Book
• Further Information: Note: Tshilidzi Marwala and Ilyes Boulkaibet (University of Johannesburg, South Africa), Sondipon Adhikari (Swansea University, UK).
• Authors: Marwala, Tshilidzi, 1971-; Boulkaibet, Ilyes, 1981-; Adhikari, Sondipon
• Contents: 1. Introduction to Finite Element Model Updating 1.1 Introduction 1 1.2 Finite Element Modelling 2 1.3 Vibration Analysis 4 1.3.1 Modal Domain Data 4 1.3.2 Frequency Domain Data 4 1.4 Finite Element Model Updating 5 1.5 Finite Element Model Updating and Bounded Rationality 6 1.6 Finite Element Model Updating Methods 7 1.6.1 Direct Methods 7 1.6.1.1 Matrix Update Methods 7 1.6.1.2 Lagrange Multiplier Method 8 1.6.1.3 Optimal Matrix Methods 8 1.6.1.4 Eigenstructure Assignment Methods 8 1.6.2 Iterative Methods 9 1.6.2.1 Sensitivity Methods 9 1.6.2.2 Iterative Optimization Methods 9 1.6.3 Artificial Intelligence Methods 9 1.6.4 Uncertainty Quantification Methods 10 1.6.4.1 Perturbation Method 10 1.6.4.2 Minimum Variance Method 11 1.6.4.3 Bayesian Approaches 12 1.7 Bayesian Approach versus Maximum Likelihood Method 13 1.8 Outline of the Book 13 1.9 References 15 2. Model Selection to Finite Element Model Updating 2.1 Introduction 25 2.2 Model Selection in Finite Element Modelling 25 2.2.1 Akaike Information Criterion 26 2.2.2 Bayesian Information Criterion 26 2.2.3 Bayes Factor 26 2.2.4 Deviance Information Criterion 27 2.2.5 Particle Swarm Optimization for Model Selection 27 2.2.6 Regularization 28 2.2.7 Cross-Validation 29 2.2.8 Nested Sampling for Model Selection 29 2.3 Simulated Annealing (SA) 31 2.4 Unsymmetrical H-shaped Structure 34 2.5 Experimental Investigation 34 2.5.1 Regularization 34 2.5.2 Cross-validation 35 2.5.3 Bayes Factor and Nested Sampling 35 2.6 Conclusion 36 2.7 References 36 3. Bayesian Statistics in Structural Dynamics 3.1 Introduction 43 3.2 Bayes’ rule 46 3.3 Maximum Likelihood Method 47 3.4 Maximum a posteriori (MAP) parameter estimates 47 3.5 Laplace’s method 47 3.6 Prior, likelihood and posterior function of a simple Dynamic example 48 3.6.1 Likelihood Function 49 3.6.2 Prior Function 49 3.6.3 Posterior Function 50 3.6.4 Gaussian Approximation 51 3.7 The posterior approximation 52 3.7.1 Objective Function 52 3.7.2 Optimization Approach 53 3.7.3 Case Example 55 3.8 Sampling Approaches for Sampling Probability Distribution 3.8.1 Monte Carlo Method 56 3.8.2 Markov Chain Monte Carlo Method 57 3.8.3 Simulated Annealing 57 3.8.4 Gibbs Sampling 58 3.9 Comparison between Approaches 59 3.9.1 Numerical example 59 3.10 Conclusions 61 3.11 References 61 4. Metropolis-Hastings and Slice Sampling for Finite Element Updating 4.1 Introduction 67 4.2 Likelihood, Prior, and the Posterior Functions 68 4.3 The Metropolis-Hastings algorithm 70 4.4 The Slice Sampling Algorithm 71 4.5 Statistical Measures 75 4.6 Application 1: Cantilevered Beam 76 4.7 Application 2: Unsymmetrical H-shaped Structure 81 4.8 Conclusions 84 4.9 References 84 5. Dynamically Weighted Importance Sampling for Finite Element Updating 5.1 Introduction 89 5.2 Bayesian Modeling Approach 90 5.3 Metropolis-Hastings (M-H) Algorithm 91 5.4 Importance Sampling 92 5.5 Dynamically Weighted Importance Sampling (DWIS) 93 5.5.1 Markov Chain 94 5.5.2 Adaptive Pruned-Enriched Population Control Scheme (APEPCS) 94 5.5.3 Monte Carlo Dynamically Weighted Importance Sampling (MCDWIS) 96 5.6 Application 1: Cantilevered Beam 96 5.7 Application 2: H-shaped Structure 101 5.8 Conclusions 105 5.9 References 106 6. Adaptive Metropolis-Hastings for Finite Element Updating 6.1 Introduction 109 6.2 Adaptive Metropolis-Hastings (AMH) Algorithm 109 6.3 Application 1: Cantilevered Beam 112 6.4 Application 2: Unsymmetrical H-Shaped Beam 115 6.5 Application 3: Aircraft GARTEUR Structure 119 6.6 Conclusion 124 6.7 References 124 7. Hybrid Monte Carlo Technique for Finite Element Model Updating 7.1 Introduction 127 7.2 Hybrid Monte Carlo Method 128 7.3 Properties of the HMC Method 129 7.3.1 Time Reversibility 129 7.3.2 Volume Preservation 129 7.3.3 Energy Conservation 129 7.4 The Molecular Dynamics Algorithm 129 7.5 Improving the HMC 131 7.5.1 Choosing an Efficient Time Step 131 7.5.2 Suppressing the Random Walk in the Momentum 132 7.5.3 The Gradient Computation 132 7.6 Application 1: Cantilever Beam 133 7.7 Application 2: Unsymmetrical H-shaped Structure 137 7.8 Conclusion 140 7.9 References 140 8. Shadow Hybrid Mote Carlo Technique for Finite Element Model Updating 8.1 Introduction 143 8.2 Effect of Time-step in the Hybrid Monte Carlo Method 144 8.3 The Shadow Hybrid Monte Carlo Method 144 8.4 The Shadow Hamiltonian 146 8.5 Application: GARTEUR SM-AG19 Structure 148 8.6 Conclusion 158 8.7 References 159 9. The Separable Shadow Hybrid Monte Carlo in Finite Element Updating 9.1 Introduction 161 9.2 Separable Shadow Hybrid Monte Carlo 161 9.3 Theoretical Justifications of the S2HMC Method 164 9.4 Application 1: Unsymmetrical H-shaped Structure 165 9.5 Application 2: GARTEUR SM-AG19 Structure 170 9.6 Conclusions 177 9.7 References 177 10. Evolutionary Approach to Finite Element Model Updating 10.1 Introduction 181 10.2 The Bayesian Formulation 182 10.3 The Evolutionary MCMC Algorithm 184 10.3.1 Mutation 185 10.3.2 Crossover 186 10.3.3 Exchange 187 10.4 Metropolis-Hastings Method 187 10.5 Application: Unsymmetrical H-shaped Structure 188 10.6 Conclusion 192 10.7 References 192 11. Adaptive Markov Chain Monte Carlo Method for Finite Element Model Updating 11.1 Introduction 197 11.2 The Bayesian Theory 200 11.3 Adaptive Hybrid Monte Carlo 201 11.4 Application 1: A 3 DOF Linear System 204 11.4.1 Updating the Stiffness Parameters 204 11.5 Application 2: Unsymmetrical H-shaped Structure 207 11.5.1 H-shaped Structure Simulation 208 11.6 Conclusion 212 11.7 References 213 12. Conclusions and Further Work 12.1 Introduction 217 12.2 Further Work 218 12.2.1 Reversible Jump Monte Carlo 218 12.2.2 Multiple-try Monte Carlo 219 12.2.3 Dynamic Programming 219 12.2.4 Sequential Monte Carlo 219 12.3 References 220 A. Appendix A: Experimental Examples A.1 Application 1: Cantilevered Beam 221 A.2 The H-shaped Structure Simulation 223 A.3 Application 2: GARTEUR SM-AG19 Structure 226 A.4 References 231 B. Appendix B: Markov Chain Monte Carlo B.1 Introduction 233 B.2 Basic Definition of the Markov Chain 233 B.3 Invariant Distribution 233 B.4 Reversibility and Ergodicity 234 B.5 References 234 C. Appendix C: Gaussian Distribution C.1 Introduction 235 C.2 The Gaussian Distribution 235 C.3 Properties of the Gaussian Distribution 235 C.4 References
• Publisher Details: Chichester, West Sussex, United Kingdom : Wiley
• Publication Date: 2017
• Copyright Date: 2017
• Extent: 1 online resource (xiii, 228 pages), illustrations
• Subjects: 620.001/51825; Finite element method; Bayesian statistical decision theory; Engineering -- Mathematical models; Bayesian statistical decision theory; Engineering -- Mathematical models; Finite element method; Electronic books
• Languages: English
• ISBNs: 9781119153030; 1119153034; 9781119153016; 1119153018; 9781119153009
• Related ISBNs: 111915300X
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
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