Phát triển các phương pháp tối ưu hóa thông minh cho các bài toán cơ học

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META-HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS PHD THESIS MAJOR: ENGINEERING MECHANICS Ho Chi Minh City, 01/2021 THE WORK IS COMPLETED AT HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META-HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS MAJOR: ENGINEERING MECHANICS 13252010105 Supervisor 1: Assoc Prof NGUYEN HOAI SON Supervisor 2: Assoc Prof LE ANH THANG PhD thesis is protected in front of EXAMINATION COMMITTEE FOR PROTECTION OF DOCTORAL THESIS HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION Date……month……year…… ii ORIGINALITY STATEMENT I, Lam Phat Thuan, hereby assure that this dissertation is my own work The data and results stated in this dissertation are honest and have not been published by any works Ho Chi Minh City, January 2021 Lam Phat Thuan ACKNOWLEDGEMENTS This dissertation 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 Prof Dr Nguyen Hoai Son and Assoc Prof Le Anh Thang, especially Assoc Prof Dr 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 Civil Engineering Faculty for their great support to help me have good environment to 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 dissertation 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 [1], 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 [2] 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 i 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 [3] Therefore, reliability-based design optimization (RBDO) can be considered as an important and comprehensive strategy for finding an optimal design In this dissertation, an improved version of Differential Evolution has been first time utilized to solve for optimal fiber angle and thickness of the reinforced 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 reinforced 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 iv TÓM TẮT Hầu tốn thiết kế kỹ thuật coi toán tối ưu địi hỏi kỹ thuật tối ưu hóa để giải Trong thập kỷ qua, nhiều kỹ thuật tối ưu hóa đề xuất áp dụng để giải loạt vấn đề khác Trong số đó, thuật tốn meta-heuristic trở nên phổ biến năm gần việc giải vấn đề tối ưu hóa thiết kế nhiều loại cấu trúc với vật liệu khác Các thuật toán meta-heuristic bao gồm Genetic Algorithms, Particle Swarm Optimization, Bat Algorithm, Cuckoo Search, Differential Evolutioin, Firefly Algorithm, Harmony Search, Flower Pollination Algorithm, Ant Colony Optimization, Bee Algorithms, Jaya Algorithm nhiều thuật toán khác Trong số phương pháp đề cập trên, Differential Evolution phương pháp sử dụng rộng rãi Kể từ Storn Price [1] giới thiệu lần đầu tiên, nhiều nghiên cứu thực để cải thiện áp dụng DE việc giải vấn đề tối ưu hóa cấu trúc DE chứng minh hiệu suất tuyệt vời việc giải nhiều vấn đề kỹ thuật khác Bên cạnh thuật toán Differential Evolution, thuật toán Jaya Rao [2] đề xuất gần phương pháp hiệu áp dụng rộng rãi để giải nhiều vấn đề tối ưu hóa cho thấy hiệu suất tốt Nó đạt kết vượt trội thử nghiệm với hàm test benchmark so với phương pháp dựa dân số khác Tuy nhiên, giống nhiều thuật toán tối ưu hóa dựa dân số khác, nhược điểm DE Jaya thời gian tính tốn tối ưu chậm nhiều so với phương pháp tối ưu hóa dựa độ dốc (gradient-based algorithms) Điều DE Jaya nhiều thời gian để đánh giá hàm mục tiêu cá thể dân số Để khắc phục nhược điểm này, mạng nơ ron nhân tạo (Artificial Neural Networks) nghiên cứu để kết hợp với thuật toán meta-heuristic, Differential Evolution, để tạo thành phương pháp tiếp cận giúp giải v toán tối ưu hóa thiết kế cách hiệu Bên cạnh đó, vấn đề quan trọng thiết kế kỹ thuật thiết kế tối ưu thường bị ảnh hưởng yếu tố ngẫu nhiên Những yếu tố xảy từ nhiều nguồn khác nhau, chẳng hạn quy trình sản xuất, tính chất vật liệu mơi trường vận hành khiến cấu trúc hoạt động khơng thiết kế ban đầu, dẫn đến rủi ro cho cấu trúc [3] Do đó, tối ưu hóa thiết kế dựa độ tin cậy (Reliability-Based Design Optimization) coi chiến lược tồn diện, cần thiết để tìm kiếm thiết kế tối ưu Trong luận án này, lần phiên cải tiến phương pháp Differential Evolution sử dụng để tìm góc hướng sợi tối ưu độ dày gia cường vật liệu composite Thứ hai, Mạng nơ ron nhân tạo (ANN) tích hợp vào quy trình tối ưu hóa thuật tốn Differentail Evolution cải tiến để hình thành thuật tốn gọi thuật toán ABDE (Artificial Neural Network-Based Differential Evolution) Thuật tốn sau áp dụng để giải tốn tối ưu hóa cấu trúc composite gia cường Thứ ba, kỹ thuật lựa chọn tinh hoa (Elitist Selection Technique) sử dụng để hiệu chỉnh bước lựa chọn thuật toán Jaya ban đầu để cải thiện hội tụ thuật tốn hình thành phiên thuật toán Jaya gọi thuật toán iJaya Thuật tốn Jaya cải tiến (iJaya) sau áp dụng để giải tốn tối ưu hóa dầm Timoshenko vật liệu composite thu kết tốt Cuối cùng, thuật toán SLMDiJaya tạo thành từ kết hợp thuật toán Jaya cải tiến phương pháp vòng lặp đơn xác định (Single-Loop Deterministic Method) đề xuất công cụ để giải vấn đề Tối ưu hóa thiết kế dựa độ tin cậy Phương pháp áp dụng để tìm kiếm thiết kế tối ưu cấu trúc dầm composite Timoshenk cho kết vượt trội vi CONTENTS ORIGINALITY STATEMENT i ACKNOWLEDGEMENTS ii ABSTRACT iii CONTENTS vii NOMENCLATURE x LIST OF TABLES .xiii LIST OF FIGURES .xiv CHAPTER 1.1 An overview on research direction of the thesis .1 1.2 Motivation of the research 1.3 Goals of the dissertation 1.4 Research scope of the dissertation 1.5 Outline 1.6 Concluding remarks CHAPTER 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 reinforced composite plate 23 CHAPTER 26 vi 3.1 Overview of Metaheuristic Optimization 26 3.1.1 Meta-heuristic Algorithm in Modeling 27 3.1.2 Meta-heuristic Algorithm in Optimization 31 3.2 Solving Optimization problems using improved Differential Evolution 41 3.2.1 Brief on the Differential Evolution algorithm [14], [129] .42 3.2.2 The modified algorithm Roulette-Wheel-Elitist Differential Evolution 43 3.3 Solving Optimization problems using improved Jaya algorithm .44 3.3.1 Jaya Algorithm 44 3.2.2 Improvement version of Jaya algorithm 45 3.4 Reliability-based design optimization using a global single loop deterministic method 46 3.4.1 Reliability-based optimization problem formulation 48 3.4.2 A global single-loop deterministic approach 49 CHAPTER 53 4.1 Fundamental theory of Neural Network .53 4.1.1 Basic concepts on Neural Networks [146] 55 4.1.2 Neural Network Structure .56 4.1.3 Neural Network Design Steps 60 4.1.4 Levenberg-Marquardt training algorithm .61 4.1.5 Over fitting, Over training .63 4.2 Artificial Neural Network based meta-heuristic optimization methods 65 CHAPTER 68 vi