Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models

OpenMDAO: Framework for Flexible Multidisciplinary Design, Analysis and Optimization Methods

The OpenMDAO project is underway at NASA to develop a framework which simplifies the implementation of state-of-the-art tools and methods for multidisciplinary design, analysis and optimization. Foremost, OpenMDAO has been designed to handle variable problem formulations, encourage reconfigurability, and promote model reuse. This work demonstrates the concept of iteration hierarchies in OpenMDAO to achieve a flexible environment for supporting advanced optimization methods which include adaptive sampling and surrogate modeling techniques. In this effort, two efficient global optimization methods were applied to solve a constrained, single-objective and constrained, multiobjective version of a joint aircraft/engine sizing problem. The aircraft model, NASA's nextgeneration advanced single-aisle civil transport, is being studied as part of the Subsonic Fixed Wing project to help meet simultaneous program goals for reduced fuel burn, emissions, and noise. This analysis serves as a realistic test problem to demonstrate the flexibility and reconfigurability offered by OpenMDAO

Numerical Simulation and Customized DACM Based Design Optimization

PhD thesis in Offshore technologyThe diverse numerical modelling, analysis and simulation tools that have been developed and introduced to markets are intended to perform the virtual design and testing of products and systems without the construction of physical prototypes. Digital prototyping in the form of computer modelling and simulation are important means of numerical model predictions, i.e. design validation and verification. However, as the tools advance to more precise and diverse applications, the operation eventually becomes more complex, computationally expensive and error prone; this is particularly true for complex multi-disciplinary and multidimensional problems; for instance, in multi-body dynamics, Fluid-Structure Interaction (FSI) and high-dimensional numerical simulation problems. On the other hand, integrating design optimization operations into the product and system development processes, through the computer based applications, makes the process even more complex and highly expensive. This thesis analyses and discusses causes of complexity in numerical modelling, simulation and optimization operations and proposes new approaches/frameworks that would help significantly reduce the complexity and the associated computational costs. Proposed approaches mainly integrate, simplify and decompose or approximate complex numerical simulation based optimization problems into simpler, and to metamodel-based optimization problems. Despite advancing computational technologies in continuum mechanics, the design and analysis tools have developed in separate directions with regard to ‘basis functions’ of the technologies until recent developments. Basis functions are the building blocks of every continuous function. Continuous functions in every computational tool are linear combinations of specific basis functions in the function space. Since first introduced, basis functions in the design and modelling tools have developed so rapidly that various complex physical problems can today be designed and modelled to the highest precision. On the other hand, most analysis tools still utilize approximate models of the problems from the latter tools, particularly if the problem involves complex smooth geometric designs. The existing gap between the basis functions of the tools and the increasing precision of models for analysis introduce tremendous computational costs. Moreover, to transfer models from one form of basis function to another, additonal effort is required. The variation of the basis functions also demands extra effort in numerical simulation based optimization processes. This thesis discusses the recently developed integrated modelling and analysis approach that utilizes the state-of-the-art basis function (NURBS function) for both design and analysis. A numerical simulation based shape optimization framework that utilizes the state-of-the-art basis function is also presented in a study in the thesis. One of the common multidisciplinary problem that involves multiple models of domains in a single problem, fluid-structure interaction (FSI) problem, is studied in the thesis. As the name implies, the two models of domains involved in any FSI problems are fluid and structure domain models. In order to solve the FSI problems, usually three mathematical components are needed: namely, i) fluid dynamics model, ii) structural mechanics model and, iii) the FSI model. This thesis presents the challenges in FSI problems and discusses different FSI approaches in numerical analysis. A comparative analysis of computational methods, based on the coupling and temporal discretization schemes, is discussed using a benchmark problem, to give a better understanding of what a multidisciplinary problem is and the challenge for design optimizations that involve such problems. [...

Resistance reduction of a military ship by variable-accuracy metamodel-based multidisciplinary robust design optimization

A method for simulation-based multidisciplinary robust design optimization (MRDO) affected by uncertainty is presented, based on variable-accuracy metamodelling. The approach encompasses a variable level of refinement of the design of experiments (DoE) used for the metamodel training, a variable accuracy for the uncertainty quantification (UQ), and a variable level of coupling between disciplines for the multidisciplinary analysis (MDA). The results of the present method are compared with a standard MRDO, used as a benchmark and solved by fully coupled MDA and fully accurate UQ, without metamodels. The hull-form optimization of the DTMB 5415 subject to stochastic speed is presented. A two-way steady coupled system is considered, based on hydrodynamics and rigid-body equation of motion. The objective function is the expected value of the total resistance, and the design variables pertain to the modification of the hull form. The effectiveness and the efficiency of the present method are evaluated in terms of optimal design performances and number of simulations required to achieve the optimal design

A comprehensive literature classification of simulation optimisation methods

Simulation Optimization (SO) provides a structured approach to the system design and configuration when analytical expressions for input/output relationships are unavailable. Several excellent surveys have been written on this topic. Each survey concentrates on only few classification criteria. This paper presents a literature survey with all classification criteria on techniques for SO according to the problem of characteristics such as shape of the response surface (global as compared to local optimization), objective functions (single or multiple objectives) and parameter spaces (discrete or continuous parameters). The survey focuses specifically on the SO problem that involves single per-formance measureSimulation Optimization, classification methods, literature survey

APPROXIMATION ASSISTED MULTIOBJECTIVE AND COLLABORATIVE ROBUST OPTIMIZATION UNDER INTERVAL UNCERTAINTY

Optimization of engineering systems under uncertainty often involves problems that have multiple objectives, constraints and subsystems. The main goal in these problems is to obtain solutions that are optimum and relatively insensitive to uncertainty. Such solutions are called robust optimum solutions. Two classes of such problems are considered in this dissertation. The first class involves Multi-Objective Robust Optimization (MORO) problems under interval uncertainty. In this class, an entire system optimization problem, which has multiple nonlinear objectives and constraints, is solved by a multiobjective optimizer at one level while robustness of trial alternatives generated by the optimizer is evaluated at the other level. This bi-level (or nested) MORO approach can become computationally prohibitive as the size of the problem grows. To address this difficulty, a new and improved MORO approach under interval uncertainty is developed. Unlike the previously reported bi-level MORO methods, the improved MORO performs robustness evaluation only for optimum solutions and uses this information to iteratively shrink the feasible domain and find the location of robust optimum solutions. Compared to the previous bi-level approach, the improved MORO significantly reduces the number of function calls needed to arrive at the solutions. To further improve the computational cost, the improved MORO is combined with an online approximation approach. This new approach is called Approximation-Assisted MORO or AA-MORO. The second class involves Multiobjective collaborative Robust Optimization (McRO) problems. In this class, an entire system optimization problem is decomposed hierarchically along user-defined domain specific boundaries into system optimization problem and several subsystem optimization subproblems. The dissertation presents a new Approximation-Assisted McRO (AA-McRO) approach under interval uncertainty. AA-McRO uses a single-objective optimization problem to coordinate all system and subsystem optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the subsystem objective functions. In this way, AA-McRO is able to explore the design space and obtain optimum design solutions more efficiently compared to a previously reported McRO. Both AA-MORO and AA-McRO approaches are demonstrated with a variety of numerical and engineering optimization examples. It is found that the solutions from both approaches compare well with the previously reported approaches but require a significantly less computational cost. Finally, the AA-MORO has been used in the development of a decision support system for a refinery case study in order to facilitate the integration of engineering and business decisions using an agent-based approach

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo

Structural model updating based on metamodel using modal frequencies

Modal frequencies are often used in structural model updating based on the finite element model, and metamodel technique is often applied to the corresponding optimization process. In this work, the Kriging model is used as the metamodel. Firstly, the influence of different correlation functions of Kriging model is inspected, and then the approximate capability of Kriging model is investigated via inspecting the approximate accuracy of nonlinear functions. Secondly, a model updating procedure is proposed based on the Kriging model, and the samples for constructing Kriging model are generated via the method of Optimal Latin Hypercube. Finally, a typical frame structure is taken as a case study and demonstrates the feasibility and efficiency of the proposed approach. The results show the Kriging model can match the target functions very well, and the finite element model can achieve accurate frequencies and can reliably predict the frequencies after model updating