Development of meta heuristic of optimization methods for mechanics problems

Development of meta heuristic of optimization methods for mechanics problems Development of meta heuristic of optimization methods for mechanics problems Development of meta heuristic of optimization methods for mechanics problems Development of meta heuristic of optimization methods for mechanics problems

Contents Originality Statement i Acknowledgements i Abstract ii Contents iv Nomenclature vii List of Tables xii List of Figures xiii Chapter 1: LITERATURE REVIEW .1 1.1 An overview on research direction of the thesis .1 1.2 Motivation of the research 1.3 Goals of the thesis 1.4 Research scope of the thesis 1.5 Outline 1.6 Contributions of the thesis Chapter 2: FUNDAMENTAL THEORY OF COMPOSITE STRUCTURE IN DESIGN AND OPTIMIZATION 10 2.1 Introduction to Composite Materials 10 2.1.1 Basic concepts and applications of Composite Materials .10 2.1.2 Overview of Composite Material in Design and Optimization 16 2.2 Analysis of Timoshenko composite beam 18 2.2.1 Exact analytical displacement and stress 18 2.2.2 Boundary-condition types .22 2.3 Analysis of stiffened composite plate .23 Chapter 3: RELIABILITY-BASED OPTIMIZATION METHODS WITH IJAYA AND IMPROVED DIFFERENTIAL EVOLUTION .29 3.1 Overview of Metaheuristic Optimization 29 3.1.1 Meta-heuristic Algorithm in Modeling .30 3.1.2 Meta-heuristic Algorithm in Optimization 33 iv 3.2 Solving Optimization problems using improved Differential Evolution 43 3.2.1 Brief on the Differential Evolution algorithm [12], [128] .43 3.2.2 The modified algorithm Roulette-Wheel-Elitist Differential Evolution 44 3.3 Solving Optimization problems using improved Jaya algorithm 45 3.3.1 Jaya Algorithm 45 3.2.2 Improvement version of Jaya algorithm 47 3.4 Reliability-based design optimization using a global single loop deterministic method .48 3.4.1 Reliability-based optimization problem formulation 50 3.4.2 A global single-loop deterministic approach 51 Chapter 4: FUNDAMENTAL THEORY OF NEURAL NETWORK 55 4.1 Fundamental theory of Neural Network 55 4.1.1 Basic concepts on Neural Networks [145] 57 4.1.2 Neural Network Structure 58 4.1.3 Neural Network Design Steps 62 4.1.4 Levenberg-Marquardt training algorithm .63 4.1.5 Over fitting, Over training 65 4.2 Artificial Neural Network based meta-heuristic optimization methods 67 Chapter 5: DEVELOPMENTS OF META-HEURISTIC OPTIMIZATION METHODS 70 5.1 Verification of iDE algorithm 70 5.1.1 A 10-bars planar truss structure: 70 5.1.2 A 200-bars truss structure Error! Bookmark not defined 5.1.3 A 72-bar space truss structure 74 5.1.4 A 120-bar space truss structure: .77 5.2 Static analysis of the stiffened composite plate .79 v 5.3 The effective of the improved Differential Evolution algorithm 81 5.4 Optimization of stiffened composite plate .82 5.4.1 Thickness optimization of stiffened Composite plate 82 5.4.2 Artificial neural network-based optimization of stiffened composite plate 84 5.5 Deterministic optimization of composite beam .87 5.5.1 Optimal design with variables: b and h 89 5.5.2 Optimal design with variables: b and ti 92 5.6 Reliability-based optimization design of Timoshenko composite beam 95 5.6.1 Verification of SLDM-iJaya .96 5.6.2 Reliability-based lightweight design 97 Chapter 6: CONCLUSIONS AND RECOMMENDATIONS 102 6.1 Conclusions and Remarks 102 6.2 Recommendations and future works .106 REFERENCES 107 List of Publications 122 vi Nomenclature Latin Symbols b The width of the composite beam Ci Indefinite integration constants Cij Matrix of stiffness CR Crossover control parameter d degree of freedom of each node of the plate d st degree of freedom of each node of the beam D Number of design variables Dm ,Dmb ,Db ,Ds Material matrices of composite plate Dbst , Dsts Material matrices of composite beam e Distance from the middle plane of the plate E Young modulus f Loading vector G Shear modulus h,t The thickness of the composite beam/plate K Stiffness matrix of the stiffened composite plate L Length of the composite beam m Number of constraint satisfactions My Bending moment about the y axis N Number of layers of composite materials NP Size of population Np The total nodes of plate Ns The total nodes of stiffening beam Nx Normal force along the x axis p Vector of random parameters vii q(x) Transversal force on the composite beam Q Matrix of material stiffness coefficients Qz Shear force along the z axis S Matrix of compliance T Coordinate transformation matrix u(x), w(x) Displacement field of the composite beam U Total energy strain of stiffened composite plate UP Strain energy of composite plate U st Strain energy of composite stiffener x Vector of design variables X Population set wji Vector of weights  xy Shear strain in xy direction  yz Shear strain in yz direction  xz Shear strain in xz direction x Mean vector of x j Distance between feasible and infeasible design region Greek symbols  Angle between x-axis and r-axis j Distance between feasible and infeasible design region   Poison’s ratio Natural frequency  Mass density θ Vector of random design variables and random parameters i Fiber orientations of composite layers viii  Shear correction factor κb Bending strains of composite plate  The transforming matrix of beam nodes and plate nodes  Stress field  xx Normal stress in x direction  yy Normal stress in y direction γ Shear strains of composite plate  xy Shear stress in xy direction  yz Shear stress in yz direction  xz Shear stress in xz direction  Strain field ε0 Membrane strains of composite plate  xx Normal strain in x direction  yy Normal strain in y direction  xy Shear strain in xy direction  yz Shear strain in yz direction  xz Shear strain in xz direction i (r ) Linear shape function of bar element x Mean vector of x n Approximately normalized gradient vector Abbreviations 2D Two dimension 3D Three dimension ABC Artificial Bee Colony ix ABDE Artificial neural network-Based Differential Evolution ACO Ant Colony Optimization ADO Approximate Deterministic Optimization ANN Artificial Neural Network ASCHEA Adaptive Segregational Constraint Handling Evolutionary Algorithm BBO Biogeography Based Optimization C-L Cantiliver/Fixed-free CS Cuckoo Search CS-DSG3 Cell-Smoothed Discrete Shear Gap technique using triangle finite element DE Differential Evolution DLM Double-Loop Methods DOF Degree Of Freedom EA Evolutionary Algorithms EP Evolution Programming ES Evolution Strategy FA Firefly Algorithms FEM Finite Element Method F-F Fixed-Fixed F-P Fixed-Pinned GA Genetic Algorithm GP Genetic Programming GSA Gravitational Search Algorithm HM Homomorphous Mapping HS Harmony Search iDE improved Differential Evolution MLP Multi-Layer Perceptron MPP Most Probable Point x NNs Neural Networks P-P Pinned-pinned PSO Particle Swarm Optimization RBDO Reliability Based Design Optimization RBF Radial Basis Function SLDM Single Loop Deterministic Method SA Simulated Annealing SI Swarm Intelligence SLP Sequential Linear Programming SMES Simple Multi-Membered Evolution Strategy SQP Sequential Quadratic Programming VBA Virtual Bee Algorithm xi List of Tables TABLES PAGE Table Parameters for 10 bars truss 71 Table The comparison results keep the solution from the improved DE algorithm with other methods for the 10-bar flattening problem 72 Table Parameter for 200-bars truss structure 74 Table Results of the comparison between the solution from the improved DE algorithm and other methods for the problem of optimizing the 200-bar scaffold problem 75 Table 5 Parameters for 72-bars space truss structure 76 Table Comparison between the solution from iDE algorithm with other methods for the 72-bars space truss problem 77 Table Parameters for 120-bars arch space truss structure 78 Table Results of comparison of solutions from the improved DE algorithm with other methods for the optimization problem of space bar of 120 bars .79 Table Comparison of central deflection (mm) of the simply-supported square stiffened composite plates 80 Table 10 The optimal results of two problems 82 Table 11 Optimal thickness results for stiffened composite plate problems .84 Table 12 Sampling and overfitting checking error .85 Table 13 Comparison of the accuracy and computational time between DE and ABDE 86 Table 14 Material properties of lamina .89 Table 15 Comparison of optimal design with continuous design variables 90 Table 16 Comparison of optimal design with discrete design variables .92 Table 17 Comparison of optimization results of the mathematical problem 96 Table 18 Optimal results of reliability based lightweight design with different level of reliability 99 xii List of Figures FIGURES PAGE Figure Types of fiber-stiffened composites 12 Figure 2 Boeing 787 - first commercial airliner with composite fuselage and wings (Courtesy of Boeing Company.) 13 Figure Composite mixer drum on concrete transporter truck weighs 2000 lbs less than conventional steel mixer drum 14 Figure Pultruded fiberglass composite structural elements (Courtesy of Strongwell Corporation.) 15 Figure Composite wind turbine blades (Courtesy of GE Energy.) 15 Figure Composite laminated beam model 19 Figure Free-body diagram 19 Figure The material and laminate coordinate system 20 Figure A composite plate stiffened by an r-direction beam .24 Figure Source of inspiration in meta-heuristic optimization algorithms 34 Figure Illustration of the feasible design region 52 Figure Biological neuron 55 Figure Perceptron neuron of Pitts and McCulloch 56 Figure Applying a model based on field data 57 Figure 4 The relationship between Machine Learning and the neural network 58 Figure A Multi-layer perceptron network model .59 Figure Single node in an MLP network 59 Figure Tanh and Sigmoid function 60 Figure A multi-layer perceptron with one hidden layer Both layers use the same activation function g 61 Figure Diagram for the training process of a neural network with the LevenbergMarquardt algorithm 65 Figure 10 Dividing the training data for the validation process 67 xiii 225–233, 2004 [32] R Yang and L Gu, “Experience with approximate reliability-based optimization methods,” Struct Multidiscip Optim, vol 26, pp 152–59, 2004, doi: 10.1007/s00158-003-0319-2 [33] T Zou and S Mahadevan, “A direct decoupling approach for efficient reliability-based design optimization,” Struct Multidiscip Optim., vol 31, no 13, pp 190–200, 2006 [34] P B Thanedar and S Kodiyalam, “Structural optimization using probabilistic constraints,” Struct Multidiscip Optim., 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International Journal T Lam-Phat, V Ho-Huu, S Nguyen-Ngoc, S Nguyen-Hoai, Trung Nguyen-Thoi Deterministic and reliability-based lightweight design of Timoshenko composite beams Engineering with Computers, 2020, https://doi.org/10.1007/s00366-02000946-8 T Lam-Phat, S Nguyen-Hoai, V Ho-Huu, Q Nguyen, T Nguyen-Thoi An Artificial Neural Network-Based Optimization of Stiffened Composite Plate Using A New Adjusted Differential Evolution Algorithm Proceedings of the International Conference on Advances in Computational Mechanics 2017 pp 229-242 (Part of the Lecture Notes in Mechanical Engineering book series (LNME)) Link: https://link.springer.com/chapter/10.1007/978-981-10-7149-2_16 Q Nguyen, S Nguyen-Hoai, T Chuong-Thiet, T Lam-Phat Optimization of the Longitudinal Cooling Fin by Levenberg–Marquardt Method Proceedings of the International Conference on Advances in Computational Mechanics 2017 pp 217227 (Part of the Lecture Notes in Mechanical Engineering book series (LNME)) Link: https://link.springer.com/chapter/10.1007/978-981-10-7149-2_15 National Journal Lam Phat Thuan, Nguyen Nhat Phi Long, Nguyen Hoai Son, Ho Huu Vinh, Le Anh Thang Global Optimization of Laminzation Composite Beams Using An Improved Differential Evolution Algorithm Journal of Science and Technology in Civil Engineering NUCE 2020 14 (1): 54–64 International Conference 122 Thuan Lam-Phat, Son Nguyen-Hoai, Vinh Ho-Huu, Trung Nguyen-Thoi Optimization of stiffened composite plate using adjusted different evolution algorithm Proceeding of the international conference on computational methods (Vol.3, 2016), Berkeley, CA, USA National Conference Thuan Lam-Phat, Son Nguyen-Hoai, Vinh Ho-Huu, Trung Nguyen-Thoi Optimization analysis of stiffened composite plate by adjusted different evolution Hội nghị Khoa học – Cơng nghệ tồn quốc khí 2015 Lâm Phát Thuận, Nguyễn Hoài Sơn, Lê Anh Thắng, Hồ Hữu Vịnh Tối ưu hóa góc hướng sợi Composite gia cường dùng thuật toán Differential Evolution kết hợp mạng thần kinh nhân tạo Hội nghị học toan quốc lần thứ X, 8-9/12/2017) Other papers T Nguyen-Thoi, T Rabczuk, T Lam-Phat, V Ho-Huu, P Phung-Van (2014) Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3) Theoretical and Applied Fracture Mechanics Vol.72, 150-163 Link: https://www.sciencedirect.com/science/article/pii/S016784421400041X Nguyen-Thoi, T., Ho-Huu, V., Dang-Trung, H., Bui-Xuan, T., Lam-Phat, T (2013) Optimization analysis of stiffened composite plate by sequential quadratic programming Journal of Science and Technology, Vol 51(4B), p 156-165 10 Nguyen Thoi Trung, Bui Xuan Thang, Ho Huu Vinh, Lam Phat Thuan, Ngo Thanh Phong An Effective Algorithm For Reliability-Based Optimization Of Stiffened 123 Mindlin Plate Vietnam Journal of Mechanics, VAST, Vol 35, No (2013), pp 335 – 346 124 ... Artificial Neural Network based meta- heuristic optimization methods 67 Chapter 5: DEVELOPMENTS OF META- HEURISTIC OPTIMIZATION METHODS 70 5.1 Verification of iDE algorithm 70... traditional optimization methods usually not work well The current trend is to use evolutionary algorithms and meta- heuristic optimization methods to tackle such nonlinear optimization problems Meta- heuristic. .. performed as usual 28 Chapter 3: RELIABILITY-BASED OPTIMIZATION METHODS WITH IJAYA AND IMPROVED DIFFERENTIAL EVOLUTION 3.1 Overview of Metaheuristic Optimization In meta- heuristic algorithms, meta-