A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

2019 ◽  
Vol 25 (9) ◽  
pp. 1455-1474 ◽  
Author(s):  
Lei Wang ◽  
Haijun Xia ◽  
Yaowen Yang ◽  
Yiru Cai ◽  
Zhiping Qiu
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Large Scale ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Content Type ◽  
Continuum Structures ◽  
Novel Approach ◽  
Design Variables ◽  
Interval Uncertainties

Purpose The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Topology optimization of continuum structures with uncertain-but-bounded parameters for maximum non-probabilistic reliability of frequency requirement

2015 ◽  
Vol 23 (16) ◽  
pp. 2557-2566 ◽  
Author(s):  
Bin Xu ◽  
Lei Zhao ◽  
Yi Min Xie ◽  
Jiesheng Jiang
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Mass Density ◽  
Limit State ◽  
Optimization Procedure ◽  
State Equation ◽  
Outer Loop ◽  
Continuum Structures ◽  
Beso Method

A method for the non-probabilistic reliability optimization on frequency of continuum structures with uncertain-but-bounded parameters is proposed. The objective function is to maximize the non-probabilistic reliability index of frequency requirement.The corresponding bi-level optimization model is built, where the constraints are applied on the material volume in the outer loop and the limit state equation in the inner loop. The non-probabilistic reliability index of frequency requirement is derived by the analytical method for the continuum structure with the uncertain elastic module and mass density. Further, the sensitivity of the non-probabilistic reliability index with respect to the design variables is analyzed. The topology optimization in the outer loop is performed by a bi-directional evolutionary structural optimization (BESO) method, where the numerical techniques and the optimization procedure of BESO method are presented. Numerical results show that the proposed BESO method is efficient, and convergent optimal solutions can be achieved for a variety of optimization problems on frequency non-probabilistic reliability of continuum structures.

Topology and Sizing Optimization of Micromixers Using Graph-Theoretical Representation and Genetic Algorithm

2017 ◽  
Author(s):  
Mitsuo Yoshimura ◽  
Koji Shimoyama ◽  
Takashi Misaka ◽  
Shigeru Obayashi
Keyword(s):  
Genetic Algorithm ◽  
Topology Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Kriging Model ◽  
Local Optimum ◽  
Sizing Optimization ◽  
Local Optima ◽  
Novel Approach ◽  
Design Variables

This paper proposes a novel approach for fluid topology optimization using genetic algorithm. In this study, the enhancement of mixing in the passive micromixers is considered. The efficient mixing is achieved by the grooves attached on the bottom of the microchannel and the optimal configuration of grooves is investigated. The grooves are represented based on the graph theory. The micromixers are analyzed by a CFD solver and the exploration by genetic algorithm is assisted by the Kriging model in order to reduce the computational cost. Three cases with different constraint and treatment for design variables are considered. In each case, GA found several local optima since the objective function is a multi-modal function and each local optimum revealed the specific characteristic for efficient mixing in micromixers. Moreover, we discuss the validity of the constraint for optimization problems. The results show a novel insight for design of micromixer and fluid topology optimization using genetic algorithm.

Large-scale economic load dispatch using squirrel search algorithm

2020 ◽  
Vol 14 (6) ◽  
pp. 1351-1380
Author(s):  
Sakthivel V.P. ◽  
Suman M. ◽  
Sathya P.D.
Keyword(s):  
Power Plants ◽  
Large Scale ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Technique ◽  
Research Work ◽  
Superior Performance ◽  
Economic Load Dispatch ◽  
Fuel Cost ◽  
Content Type

Purpose Economic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants. Design/methodology/approach The suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately. Findings Empirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems. Practical implications This study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning. Originality/value To the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

2017 ◽  
Vol 09 (07) ◽  
pp. 1750092 ◽  
Author(s):  
Xingjun Gao ◽  
Lijuan Li ◽  
Haitao Ma
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Process ◽  
Continuum Structures ◽  
Design Evolution ◽  
Buckling Constraints ◽  
Load Factors ◽  
Structural Compliance ◽  
Parameter Values

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

Robust topology optimization for continuum structures with random loads

2018 ◽  
Vol 35 (2) ◽  
pp. 710-732 ◽  
Author(s):  
Jie Liu ◽  
Guilin Wen ◽  
Qixiang Qing ◽  
Fangyi Li ◽  
Yi Min Xie
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Computational Time ◽  
Optimization Approach ◽  
Random Load ◽  
Content Type ◽  
Continuum Structures ◽  
Robust Topology Optimization ◽  
Random Loads ◽  
Expansion Technique

Purpose This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method. Design/methodology/approach An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers. Findings The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions. Originality/value A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jianhua Zhou ◽  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Quadratic Programming ◽  
Robust Optimization ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Critical Role ◽  
Interval Uncertainty ◽  
Design Solution ◽  
Novel Approach ◽  
Design Variables ◽  
Feasibility Robustness

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, sequential quadratic programming for robust optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

scholarly journals Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Debiao Meng ◽  
Xiaoling Zhang ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Huanwei Xu
Keyword(s):  
Interaction Design ◽  
Large Scale ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Design Parameters ◽  
Large Scale Systems ◽  
Interaction Prediction ◽  
Design Variables ◽  
Subsystem Level

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.

An effective members-adding method for truss topology optimization based on principal stress trajectories

2017 ◽  
Vol 34 (6) ◽  
pp. 2088-2104 ◽  
Author(s):  
Ge Gao ◽  
Yaobin Li ◽  
Hui Pan ◽  
Limin Chen ◽  
Zhenyu Liu
Keyword(s):  
Topology Optimization ◽  
Principal Stress ◽  
Large Scale ◽  
Truss Topology Optimization ◽  
Force Transmission ◽  
Ground Structure ◽  
Element Analysis ◽  
Content Type ◽  
Truss Topology ◽  
Nodal Displacements

Purpose The purpose of this paper is to provide an effective members-adding method for truss topology optimization in plastic design. Design/methodology/approach With the help of the distribution of principal stress trajectories, obtained by finite element analysis of the design domain, ineffective zones for force transmission paths can be found, namely, areas whose nodes may have ersatz nodal displacements. Members connected by these nodes are eliminated and the reduced ground structure is used for optimization. Adding members in short to long order and limiting the number of members properly with the most strained ones added, large-scale truss problems in one load case and multiple-load cases are optimized. Findings Inefficient members (i.e. bars that fulfil the adding criterion but make no contribution to the optimal structure) added to the ground structure in each iterative step are reduced. Fewer members are used for optimization than before; therefore, faster solution convergence and less computation time are achieved with the optimized result unchanged. Originality/value The proposed members-adding method in the paper can alleviate the phenomenon of ersatz nodal displacements, enhance computational efficiency and save calculating resources effectively.

scholarly journals Large-Scale Truss Topology and Sizing Optimization by an Improved Genetic Algorithm with Multipoint Approximation

2021 ◽  
Vol 12 (1) ◽  
pp. 407
Author(s):  
Tianshan Dong ◽  
Shenyan Chen ◽  
Hai Huang ◽  
Chao Han ◽  
Ziqi Dai ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Approximation Technique ◽  
Discrete Topology ◽  
Improved Genetic Algorithm ◽  
Approximation Accuracy ◽  
Design Variables ◽  
Metaheuristic Methods ◽  
Multipoint Approximation

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.

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