Luận án Tiến sĩ: Phát triển phương pháp tối ưu hóa Meta-Heuristic cho bài toán cơ học

Originality Statement I, Lam Phat Thuan, hereby assure that this thesis is my own work. The data and results stated in this thesis are honest and have not been published by any works. Ho Chi Minh City, May 2021 Lam Phat Thuan Acknowledgements This thesis has been carried out in the Faculty of Civil Engineering, HCM City University of Technology and Education, Viet Nam. The process of conducting this thesis brings excitement but has quite a few challenges and difficulties.

And I can say without hesitation that it has been finished thanks to the encouragement, support and help of my professors and colleagues. First of all, I would like to express my deepest gratitude to Assoc. Nguyen Hoai Son and Assoc. Le Anh Thang, especially Assoc.

Nguyen Hoai Son from GACES Group, Ho Chi Minh City University of Technology and Education, Vietnam for having accepted me as their PhD student and for the enthusiastic guidance and mobilization during my research. Secondly, I would like also to acknowledge Msc. Ho Huu Vinh for his troubleshooting and the cooperation in my study. Furthermore, I am grateful to Faculty of Civil Engineering for their great support to help me have good environment to do my research.

Thirdly, I take this chance to thank all my nice colleagues at the Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, for their professional advice and friendly support. Finally, this thesis is dedicated to my parents who have always given me valuable encouragement and assistance. Lam Phat Thuan i Abstract Almost all design problems in engineering can be considered as optimization problems and thus require optimization techniques to solve. During the past few decades, many optimization techniques have been proposed and applied to solve a wide range of various optimization problems.

Among them, meta-heuristic algorithms have gained huge popularity in recent years in solving design optimization problems of many types of structure with different materials. These meta-heuristic algorithms include genetic algorithms (GA), particle swarm optimization (PSO), bat algorithm (BA), cuckoo search (CS), differential evolution (DE), firefly algorithm (DA), harmony search (HS), flower pollination algorithm (FPA), ant colony optimization (ACO), bee algorithms (BA), Jaya algorithm and many others. Among the methods mentioned above, the Differential Evolution is one of the most widely used methods. Since it was first introduced in 1997 by Storn and Price, many studies have been carried out to improve and apply DE in solving structural optimization problems.

The DE has demonstrated excellently performance in solving many different engineering problems. Besides the Differential Evolution algorithm, the Jaya algorithm recently proposed by Rao in 2016 is also an effective and efficient methods that has been widely applied to solve many optimization problems and showed its good performance. It gains dominate results when being tested with benchmark test functions in comparison with other meta-heuristic methods. However, like many other population-based optimization algorithms, one of the disadvantages of DE and Jaya is that the computational time obtaining optimal solutions is much slower than the gradient-based optimization methods.

This is because DE and Jaya takes a lot of time evaluating the fitness of individuals in the population. To overcome this disadvantage, Artificial Neuron Networks (ANN) are studied to combine with the meta-heuristic algorithms, such as Differential Evolution, to form a new approach which has the ability to solve the design optimization effectively. Moreover, one of the most important issues in engineering design is that the optimal designs are often effected by uncertainties which can be occurred from various sources, such as ii manufacturing processes, material properties and operating environments. These uncertainties may cause structures to improper performance as in the original design, and hence may result in risks to structures.

Therefore, reliability-based design optimization (RBDO) can be considered as an important and comprehensive strategy for finding an optimal design. In this thesis, an improved version of Differential Evolution has been first time utilized to solve for optimal fiber angle and thickness of the stiffened composite. Secondly, the Artificial Neural Network is integrated to the optimization process of the improved Differential Evolution algorithm to form a new algorithm call ABDE (ANN-based Differential Evolution) algorithm. This new algorithm is then applied to solve optimization problems of the stiffened composite plate structures.

Thirdly, an elitist selection technique is utilized to modify the selection step of the original Jaya algorithm to improve the convergence of the algorithm and formed a new version of the original Jaya called iJaya algorithm. The improved Jaya algorithm is then applied to solve for optimization problem of the Timoshenko composite beam and obtained very good results. Finally, the so-called called (SLMD-iJaya) algorithm which is the combination of the improved Jaya algorithm and the Global Single-Loop Deterministic Methods (SLDM) has been proposed as a new tool set for solving the Reliability-Based Design Optimization problems. This new method is applied to look for optimal design of Timoshenko composite beam structures with certain level of reliability.

iii Contents Originality Statement. vii List of Tables. xii List of Figures. xiii Chapter 1: LITERATURE REVIEW .1 An overview on research direction of the thesis .2 Motivation of the research .3 Goals of the thesis .4 Research scope of the thesis .6 Contributions of the thesis .9 Chapter 2: FUNDAMENTAL THEORY OF COMPOSITE STRUCTURE IN DESIGN AND OPTIMIZATION .1 Introduction to Composite Materials .1 Basic concepts and applications of Composite Materials .2 Overview of Composite Material in Design and Optimization .2 Analysis of Timoshenko composite beam.

Exact analytical displacement and stress. Boundary-condition types .3 Analysis of stiffened composite plate .23 Chapter 3: RELIABILITY-BASED OPTIMIZATION METHODS WITH IJAYA AND IMPROVED DIFFERENTIAL EVOLUTION .1 Overview of Metaheuristic Optimization .1 Meta-heuristic Algorithm in Modeling .2 Meta-heuristic Algorithm in Optimization .2 Solving Optimization problems using improved Differential Evolution 43 3.1 Brief on the Differential Evolution algorithm [12], [128] .2 The modified algorithm Roulette-Wheel-Elitist Differential Evolution .3 Solving Optimization problems using improved Jaya algorithm .2 Improvement version of Jaya algorithm .4 Reliability-based design optimization using a global single loop deterministic method. Reliability-based optimization problem formulation. A global single-loop deterministic approach .51 Chapter 4: FUNDAMENTAL THEORY OF NEURAL NETWORK .1 Fundamental theory of Neural Network .1 Basic concepts on Neural Networks [145] .2 Neural Network Structure .3 Neural Network Design Steps .4 Levenberg-Marquardt training algorithm .5 Over fitting, Over training .2 Artificial Neural Network based meta-heuristic optimization methods 67 Chapter 5: DEVELOPMENTS OF META-HEURISTIC OPTIMIZATION METHODS .1 Verification of iDE algorithm .1 A 10-bars planar truss structure: .2 A 200-bars truss structure.

Error! Bookmark not defined.3 A 72-bar space truss structure .4 A 120-bar space truss structure: .2 Static analysis of the stiffened composite plate .3 The effective of the improved Differential Evolution algorithm .4 Optimization of stiffened composite plate .1 Thickness optimization of stiffened Composite plate .2 Artificial neural network-based optimization of stiffened composite plate .5 Deterministic optimization of composite beam .1 Optimal design with variables: b and h .2 Optimal design with variables: b and ti .6 Reliability-based optimization design of Timoshenko composite beam 95 5.1 Verification of SLDM-iJaya.2 Reliability-based lightweight design .97 Chapter 6: CONCLUSIONS AND RECOMMENDATIONS .1 Conclusions and Remarks .2 Recommendations and future works .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 5. Parameters for 10 bars truss. The comparison results keep the solution from the improved DE algorithm with other methods for the 10-bar flattening problem. Parameter for 200-bars truss structure.

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. Parameters for 72-bars space truss structure. Comparison between the solution from iDE algorithm with other methods for the 72-bars space truss problem. Parameters for 120-bars arch space truss structure.

Results of comparison of solutions from the improved DE algorithm with other methods for the optimization problem of space bar of 120 bars. Comparison of central deflection (mm) of the simply-supported square stiffened composite plates. The optimal results of two problems. Optimal thickness results for stiffened composite plate problems.

12 Sampling and overfitting checking error. Comparison of the accuracy and computational time between DE and ABDE. Material properties of lamina. Comparison of optimal design with continuous design variables.

Comparison of optimal design with discrete design variables. Comparison of optimization results of the mathematical problem. Optimal results of reliability based lightweight design with different level of reliability.99 xii List of Figures FIGURES PAGE Figure 2.