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E-raamat: Probabilistic Finite Element Model Updating Using Bayesian Statistics - Applications to Aeronautical and Mechanical Engineering: Applications to Aeronautical and Mechanical Engineering [Wiley Online]

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  • Formaat: 248 pages
  • Ilmumisaeg: 25-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119153026
  • ISBN-13: 9781119153023
Teised raamatud teemal:
  • Wiley Online
  • Hind: 137,45 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Probabilistic Finite Element Model Updating Using Bayesian Statistics - Applications to Aeronautical and Mechanical Engineering: Applications to Aeronautical and Mechanical EngineeringSuurem pilt
  • Formaat: 248 pages
  • Ilmumisaeg: 25-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119153026
  • ISBN-13: 9781119153023
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119153023
Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to Aeronautical and Mechanical Engineering 

Tshilidzi Marwala and Ilyes Boulkaibet, University of Johannesburg, South Africa

Sondipon Adhikari, Swansea University, UK

 

Covers the probabilistic finite element model based on Bayesian statistics with applications to aeronautical and mechanical engineering

 

Finite element models are used widely to model the dynamic behaviour of many systems including in electrical, aerospace and mechanical engineering.

The book covers probabilistic finite element model updating, achieved using Bayesian statistics. The Bayesian framework is employed to estimate the probabilistic finite element models which take into account of the uncertainties in the measurements and the modelling procedure. The Bayesian formulation achieves this by formulating the finite element model as the posterior distribution of the model given the measured data within the context of computational statistics and applies these in aeronautical and mechanical engineering.

Probabilistic Finite Element Model Updating Using Bayesian Statistics contains simple explanations of computational statistical techniques such as Metropolis-Hastings Algorithm, Slice sampling, Markov Chain Monte Carlo method, hybrid Monte Carlo as well as Shadow Hybrid Monte Carlo and their relevance in engineering.

 

Key features:





Contains several contributions in the area of model updating using Bayesian techniques which are useful for graduate students. Explains in detail the use of Bayesian techniques to quantify uncertainties in mechanical structures as well as the use of Markov Chain Monte Carlo techniques to evaluate the Bayesian formulations.

 

The book is essential reading for researchers, practitioners and students in mechanical and aerospace engineering.
Acknowledgements x
Nomenclature xi
1 Introduction to Finite Element Model Updating
1(23)
1.1 Introduction
1(1)
1.2 Finite Element Modelling
2(2)
1.3 Vibration Analysis
4(1)
1.3.1 Modal Domain Data
4(1)
1.3.2 Frequency Domain Data
5(1)
1.4 Finite Element Model Updating
5(1)
1.5 Finite Element Model Updating and Bounded Rationality
6(1)
1.6 Finite Element Model Updating Methods
7(7)
1.6.1 Direct Methods
8(2)
1.6.2 Iterative Methods
10(1)
1.6.3 Artificial Intelligence Methods
11(1)
1.6.4 Uncertainty Quantification Methods
11(3)
1.7 Bayesian Approach versus Maximum Likelihood Method
14(1)
1.8 Outline of the Book
15(9)
References
17(7)
2 Model Selection in Finite Element Model Updating
24(18)
2.1 Introduction
24(1)
2.2 Model Selection in Finite Element Modelling
25(7)
2.2.1 Akaike Information Criterion
25(1)
2.2.2 Bayesian Information Criterion
25(1)
2.2.3 Bayes Factor
26(1)
2.2.4 Deviance Information Criterion
26(1)
2.2.5 Particle Swarm Optimisation for Model Selection
27(1)
2.2.6 Regularisation
28(1)
2.2.7 Cross-Validation
28(2)
2.2.8 Nested Sampling for Model Selection
30(2)
2.3 Simulated Annealing
32(3)
2.4 Asymmetrical H-Shaped Structure
35(2)
2.4.1 Regularisation
35(1)
2.4.2 Cross-Validation
36(1)
2.4.3 Bayes Factor and Nested Sampling
36(1)
2.5 Conclusion
37(5)
References
37(5)
3 Bayesian Statistics in Structural Dynamics
42(23)
3.1 Introduction
42(3)
3.2 Bayes' Rule
45(1)
3.3 Maximum Likelihood Method
46(1)
3.4 Maximum a Posteriori Parameter Estimates
46(1)
3.5 Laplace's Method
47(1)
3.6 Prior, Likelihood and Posterior Function of a Simple Dynamic Example
47(5)
3.6.1 Likelihood Function
49(1)
3.6.2 Prior Function
49(1)
3.6.3 Posterior Function
50(1)
3.6.4 Gaussian Approximation
50(2)
3.7 The Posterior Approximation
52(3)
3.7.1 Objective Function
52(1)
3.7.2 Optimisation Approach
52(3)
3.7.3 Case Example
55(1)
3.8 Sampling Approaches for Estimating Posterior Distribution
55(3)
3.8.1 Monte Carlo Method
55(1)
3.8.2 Markov Chain Monte Carlo Method
56(1)
3.8.3 Simulated Annealing
57(1)
3.8.4 Gibbs Sampling
58(1)
3.9 Comparison between Approaches
58(2)
3.9.1 Numerical Example
58(2)
3.10 Conclusions
60(5)
References
61(4)
4 Metropolis--Hastings and Slice Sampling for Finite Element Updating
65(19)
4.1 Introduction
65(1)
4.2 Likelihood, Prior and the Posterior Functions
66(3)
4.3 The Metropolis--Hastings Algorithm
69(2)
4.4 The Slice Sampling Algorithm
71(1)
4.5 Statistical Measures
72(2)
4.6 Application 1: Cantilevered Beam
74(4)
4.7 Application 2: Asymmetrical H-Shaped Structure
78(3)
4.8 Conclusions
81(3)
References
81(3)
5 Dynamically Weighted Importance Sampling for Finite Element Updating
84(20)
5.1 Introduction
84(1)
5.2 Bayesian Modelling Approach
85(2)
5.3 Metropolis--Hastings (M-H) Algorithm
87(1)
5.4 Importance Sampling
88(1)
5.5 Dynamically Weighted Importance Sampling
89(4)
5.5.7 Markov Chain
90(1)
5.5.2 Adaptive Pruned-Enriched Population Control Scheme
90(2)
5.5.3 Monte Carlo Dynamically Weighted Importance Sampling
92(1)
5.6 Application 1: Cantilevered Beam
93(4)
5.7 Application 2: H-Shaped Structure
97(4)
5.8 Conclusions
101(3)
References
101(3)
6 Adaptive Metropolis--Hastings for Finite Element Updating
104(18)
6.1 Introduction
104(1)
6.2 Adaptive Metropolis--Hastings Algorithm
105(3)
6.3 Application 1: Cantilevered Beam
108(3)
6.4 Application 2: Asymmetrical H-Shaped Beam
111(2)
6.5 Application 3: Aircraft GARTEUR Structure
113(6)
6.6 Conclusion
119(3)
References
119(3)
7 Hybrid Monte Carlo Technique for Finite Element Model Updating
122(16)
7.1 Introduction
122(1)
7.2 Hybrid Monte Carlo Method
123(1)
7.3 Properties of the HMC Method
124(1)
7.3.1 Time Reversibility
124(1)
7.3.2 Volume Preservation
124(1)
7.3.3 Energy Conservation
125(1)
7.4 The Molecular Dynamics Algorithm
125(2)
7.5 Improving the HMC
127(2)
7.5.7 Choosing an Efficient Time Step
127(1)
7.5.2 Suppressing the Random Walk in the Momentum
128(1)
7.5.3 Gradient Computation
128(1)
7.6 Application 1: Cantilever Beam
129(3)
7.7 Application 2: Asymmetrical H-Shaped Structure
132(3)
7.8 Conclusion
135(3)
References
135(3)
8 Shadow Hybrid Monte Carlo Technique for Finite Element Model Updating
138(17)
8.1 Introduction
138(1)
8.2 Effect of Time Step in the Hybrid Monte Carlo Method
139(1)
8.3 The Shadow Hybrid Monte Carlo Method
139(3)
8.4 The Shadow Hamiltonian
142(1)
8.5 Application: GARTEUR SM-AG19 Structure
143(9)
8.6 Conclusion
152(3)
References
153(2)
9 Separable Shadow Hybrid Monte Carlo in Finite Element Updating
155(19)
9.1 Introduction
155(1)
9.2 Separable Shadow Hybrid Monte Carlo
155(3)
9.3 Theoretical Justifications of the S2HMC Method
158(2)
9.4 Application 1: Asymmetrical H-Shaped Structure
160(5)
9.5 Application 2: GARTEUR SM-AG19 Structure
165(6)
9.6 Conclusions
171(3)
References
172(2)
10 Evolutionary Approach to Finite Element Model Updating
174(15)
10.1 Introduction
174(1)
10.2 The Bayesian Formulation
175(2)
10.3 The Evolutionary MCMC Algorithm
177(4)
10.3.1 Mutation
178(1)
10.3.2 Crossover
179(2)
10.3.3 Exchange
181(1)
10.4 Metropolis--Hastings Method
181(1)
10.5 Application: Asymmetrical H-Shaped Structure
182(3)
10.6 Conclusion
185(4)
References
186(3)
11 Adaptive Markov Chain Monte Carlo Method for Finite Element Model Updating
189(17)
11.1 Introduction
189(2)
11.2 Bayesian Theory
191(1)
11.3 Adaptive Hybrid Monte Carlo
192(3)
11.4 Application 1: A Linear System with Three Degrees of Freedom
195(3)
11.4.1 Updating the Stiffness Parameters
196(2)
11.5 Application 2: Asymmetrical H-Shaped Structure
198(4)
11.5.1 H-Shaped Structure Simulation
198(4)
11.6 Conclusion
202(4)
References
203(3)
12 Conclusions and Further Work
206(5)
12.1 Introduction
206(2)
12.2 Further Work
208(3)
12.2.1 Reversible Jump Monte Carlo
208(1)
12.2.2 Multiple-Try Metropolis-Hastings
208(1)
12.2.3 Dynamic Programming
209(1)
12.2.4 Sequential Monte Carlo
209(1)
References
209(2)
Appendix A Experimental Examples 211(8)
Appendix B Markov Chain Monte Carlo 219(3)
Appendix C Gaussian Distribution 222(4)
Index 226
Tshilidzi Marwala is a Professor of Mechanical and Electrical Engineering as well as Deputy Vice-Chancellor at the University of Johannesburg. He holds a Bachelor of Science in Mechanical Engineering from Case Western Reserve University, a Master of Mechanical Engineering from the University of Pretoria, a PhD in Engineering from Cambridge University and was a post-doctoral researcher at Imperial College (London). He is a Fellow of TWAS and a distinguished member of the ACM. His research interests are multi-disciplinary and include the applications of computational intelligence to engineering, computer science, finance, social science and medicine. He has supervised 45 Masters and 19 PhD students and has published 8 books and over 260 papers. He is an associate editor of the International Journal of Systems Science.

Dr. Ilyes Boulkaibet is currently a researcher at the University of Johannesburg. He received a PhD from the University of Johannesburg, a second MSc from Stellenbosch University, an MSc from the University of Constantine 1 Algeria, and a Bachelor of Engineering from University of Constantine 1 Algeria. Dr. Ilyes Boulkaibet has published papers in international journals and has participated in numerous conferences including the International Modal Analysis Conference. Dr. Boulkaibets research areas are multidisciplinary in nature and include uncertainty quantification in computational mechanics, dynamics of complex systems, inverse problems for linear and non-linear dynamics and control systems.

Professor Adhikari is the chair of Aerospace Engineering in the College of Engineering of Swansea University. He received his MSc from the Indian Institute of Science and a PhD from the University of Cambridge. He was a lecturer at the Bristol University and a Junior Research Fellow in Fitzwilliam College, Cambridge. He has been a visiting Professor at the University of Johannesburg, Carleton University and the Los Alamos National Laboratory . Professor Adhikari's research areas are multidisciplinary in nature and include uncertainty quantification in computational mechanics, bio- and nano-mechanics (nanotubes, graphene, cell mechanics, nano-bio sensors), dynamics of complex systems, inverse problems for linear and non-linear dynamics and vibration energy harvesting.
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