JournalTOCs

Structural and Multidisciplinary Optimization
Journal Prestige (SJR): 1.458

Citation Impact (citeScore): 3
Number of Followers: 12

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1615-1488 - ISSN (Online) 1615-147X
Published by Springer-Verlag

[2467 journals]

Interval reliability-based topology optimization of piezoelectric
structures under single-loop sequential strategy and negative feedback
control theory
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  Abstract: Abstract In this paper, an interval reliability-based topology optimization (IRBTO) of piezoelectric structure is proposed based on a single-loop strategy. Firstly, the effect of negative velocity feedback control is equivalent to damping. Then the topology optimization formula of piezoelectric structures constrained by transient dynamic response is briefly described. The interval model is employed to describe uncertainty. Considering the complex mapping relationship between the displacement response function and uncertain parameter input, the adaptive subinterval dimension-wise method is used to calculate the feasible bounds of the displacement response function. Considering the effects of interval uncertainty, the IRBTO formula of piezoelectric structure is established. The single-loop strategy is employed to decouple the IRBTO into multi-level deterministic topology optimization and uncertainty analysis. The shift value of the displacement response function in the deterministic topology optimization of the piezoelectric structure in each cycle is calculated by using the modified performance measure approach according to the reliability analysis results. The adjoint vector method is used to obtain the sensitivity of the displacement response function and design variables. Three numerical examples are given to illustrate the effectiveness and applicability of the proposed method, and the results show that different uncertainties lead to different optimization layouts.
  PubDate: 2023-03-24
Smoothing inertial method for worst-case robust topology optimization
under load uncertainty
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  Abstract: Abstract We consider a worst-case robust topology optimization problem under load uncertainty, which can be formulated as a minimization problem of the maximum eigenvalue of a symmetric matrix. The objective function is nondifferentiable where the multiplicity of maximum eigenvalues occurs. Nondifferentiability often causes some numerical instabilities in an optimization algorithm such as oscillation of the generated sequence and convergence to a non-optimal point. We use a smoothing method to tackle these issues. The proposed method is guaranteed to converge to a point satisfying the first-order optimality condition. In addition, it is a simple first-order optimization method and thus has low computational cost per iteration even in a large-scale problem. In numerical experiments, we show that the proposed method suppresses oscillation and converges faster than other existing methods.
  PubDate: 2023-03-24
Integrated topology and controller optimization using the Nyquist curve
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  Abstract: Abstract The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation.
  PubDate: 2023-03-24
A machine-learning framework for isogeometric topology optimization
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  Abstract: Abstract Isogeometric analysis has been widely applied in topology optimization in recent years, and various methods have been derived. However, most methods are accompanied by significant computational costs, which make it difficult to deal with complex models and large-scale design problems. In this paper, an isogeometric topology optimization method based on deep neural networks is proposed. The computational time of optimization can be effectively reduced while ensuring high accuracy. With the IGA-FEA two-resolution SIMP method, the machine-learning dataset can be obtained during early iterations. Unlike existing data-driven methods, online dataset generation both significantly reduces data collection time and enhances relevance to the design problem. As the iterations process, the machine learning model can be updated online by continuously collecting new data to ensure that the optimized topology structures approach the standard results. Through a series of 2D and 3D design examples, the generality and reliability of the proposed model have been verified and its time-saving advantage becomes more pronounced as the design scale increases. Furthermore, the impacts of neural network parameters on the results are studied through several controlled experiments.
  PubDate: 2023-03-24
A novel single-loop meta-model importance sampling with adaptive Kriging
for time-dependent failure probability function
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  Abstract: Abstract To learn the effect of interested distribution parameter, also the design variable of random input vector, on time-dependent failure probability, and to decouple time-dependent reliability-based design optimization (T-RBDO), estimating time-dependent failure probability function (T-FPF), a relation of time-dependent failure probability varying with the distribution parameter in interested design region, is necessary. However, estimating T-FPF is time-consuming and a challenge at present. Thus, this paper proposes a novel single-loop meta-model importance sampling with adaptive Kriging model (SL-Meta-IS-AK) to estimate T-FPF efficiently. In SL-Meta-IS-AK, for estimating the T-FPF by single-loop simulation, an optimal importance sampling probability density function (IS-PDF), which can envelope the interested distribution parameter region and be free of the distribution parameter, is constructed by an integral operation. After the Kriging model is adaptively constructed for time-dependent performance function to approach optimal IS-PDF for T-FPF by quasi-optimal one, a simple sampling strategy is designed to extract the samples of quasi-optimal IS-PDF, and a time-dependent misclassification probability function is derived to update the Kriging model adaptively until it can accurately recognize the states of all extracted samples, on which the T-FPF at the whole interested distribution parameter region can be estimated as a byproduct. Due to the single-loop simulation aided by the IS-PDF covering the interested distribution parameter region but free of the distribution parameter, the efficiency of estimating T-FPF is improved by the proposed SL-Meta-IS-AK, which is verified by presented numerical and aviation engineering examples including a wing structure and a turbine shaft structure.
  PubDate: 2023-03-23
An Armijo-based hybrid step length release first order reliability method
based on chaos control for structural reliability analysis
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  Abstract: Abstract In structural reliability analysis, the HL-RF method may not converge in some nonlinear cases. The chaos control based first-order second-moment method (CC) achieves convergence by controlling the step length with chaotic control factors, but it commonly requires very time-consuming computation. In this paper, an Armijo-based hybrid step length release method based on chaos control is proposed to surmount the above issue. An iterative control angle is introduced for the proposed method to select an adaptive adjustment step length strategy. Then, a step length release method is proposed to speed up the convergence when the iterative rotation angle is less than the rotation control angle. When the iterative rotation angle exceeds the rotation control angle, an adaptive adjustment method for step length is defined based on the Armijo rule to provide an optimal choice of adaptive step length for the iterative process and guarantee convergence. After that, the robustness and efficiency of the proposed method are proved through several examples. The examples show that the proposed method is capable of generating a suitable adaptive step length, therefore accessing a more stable and accurate solution with greater efficiency in both high and low nonlinearity cases. It can well combine the advantages of HL-RF and the CC methods, and the efficiency is further improved without sacrificing its robustness. Finally, a discussion is brought out to investigate the selection of optimal parameters and how the two step length selection strategy cooperates and co-action with one another. It can be seen that the efficiency improvement of the proposed method mainly contributed to the step length release method, while the Armijo-based adaptive adjustment method for step length guaranteed convergence.
  PubDate: 2023-03-21
Topology optimization applied to the acoustic medium inverse problem in
the time domain using integer linear programming
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  Abstract: Abstract In this paper, the acoustic inverse problem modeled in the time domain featuring wave velocity reconstruction in the presence of sharp interfaces is addressed using an integer design variable approach. The medium being reconstructed is assumed piecewise constant, with single-material obstacles embedded in a homogeneous background. The wave equation is modeled using the Finite Element Method (FEM). The inversion procedure aims at finding the parameter field that minimizes a least-squares misfit function with respect to data generated from a synthetic model. The proposed optimization methodology is based on a sequential Integer Linear Programming (ILP) formulation used in the field of Topology Optimization (TO). Since this is a gradient-based technique, the sensitivity with respect to the integer design variable is evaluated by the adjoint method. Sensitivities are modified using both damping filters and Helmholtz-type Partial Differential Equation (PDE) filters to deal with the ill-posedness that is inherent to this class of inverse problem. The integer design variable is binary, associating each point of the domain either to the homogeneous background or to the embedded obstacles. This description naturally incorporates the sharp interface hypothesis, whereas a continuous design variable may generate transition regions with intermediate values and no clearly defined boundary. The damping filter is successful in controlling instabilities by incorporating the whole optimization history to the design update. Furthermore, the generality and effectiveness of the proposed framework are evaluated by addressing 2D problems from the literature and a proposed 3D case, all featuring sharp interfaces.
  PubDate: 2023-03-21
Reliability updating with equality information using adaptive
kriging-based importance sampling
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  Abstract: Abstract Reliability updating can be interpreted by the process of reevaluating structural reliability with data stemming from structural health monitoring sensors or platforms. In virtue of the power of Bayesian statistics, reliability updating incorporates the up-to-date information within the framework of uncertainty quantification, which facilitates more reasonable and strategic decision-making. However, the associated computational cost for quantifying uncertainty can be also increasingly challenging due to the iterative simulation of sophisticated models (e.g., Finite Element Model). To expedite reliability updating with complex models, reliability updating with surrogate model has been proposed to overcome aforementioned limitations. However, the past work merely integrates reliability updating with Kriging-based crude Monte Carlo Simulation, thereby, still exists many computational limitations. For example, parameters such as the coefficient of variation of posterior failure probability, the batch size of samples, and active learning stopping criterion are not well defined or devised, which can lead to computational pitfalls. Therefore, this paper proposes RUAK-IS (Reliability Updating with Adaptive Kriging using Importance Sampling) to address the aforementioned limitations. Specifically, importance sampling is incorporated with Kriging to enable updating of small failure probability with robust estimate and error quantification. Two numerical and one practical finite element examples are investigated to explore the computational efficiency and accuracy of the proposed method. Results demonstrate the computational superiority of RUAK-IS in terms of robustness and accuracy.
  PubDate: 2023-03-20
A FreeFEM code for topological derivative-based structural optimization
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  Abstract: Abstract This article presents an educational code written in FreeFEM, based on the concept of topological derivative together with a level-set domain representation method and adaptive mesh refinement processes, to perform compliance minimization in structural optimization. The code is implemented in the framework of linearized elasticity, for both plane strain and plane stress assumptions. As a first-order topology optimization algorithm, the topological derivative is in fact used within the numerical procedure as a steepest descent direction, similar to methods based on the gradient of cost functionals. In addition, adaptive mesh refinement processes are used as part of the optimization scheme for enhancing the resolution of the final topology. Since the paper is intended for educational purposes, we start by explaining how to compute topological derivatives, followed by a step-by-step description of the code, which makes the binding of the theoretical aspects of the algorithm to its implementation. Numerical results associated with three classic examples in topology optimization are presented and discussed, showing the effectiveness and robustness of the proposed approach.
  PubDate: 2023-03-17
A robust dynamic unified multi-material topology optimization method for
functionally graded structures
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  Abstract: Abstract In this article, a density-driven unified multi-material topology optimization framework is suggested for functionally graded (FG) structures under static and dynamic responses. For this, two-dimensional solid structures and plate-like structures with/without variable thickness are investigated as design domains using multiple in-plane bi-directional FG materials (IBFGMs). In the present approach, a generally refined interpolation scheme relying upon Solid Isotropic Material with Penalization is proposed to deal with equivalent properties of IBFGMs. This methodology’s topological design variables are totally independent of all material phases. Therefore, the present method can yield separate material phases at their contiguous boundaries without intermediate density materials. The assumption of mixed interpolation of tensorial components of the 4-node shell element is employed to analyze plate elements, aiming to tackle the shear-locking phenomenon encountered as the optimal plate thickness becomes thinner. The mesh-independence filter is utilized to suppress the checkerboard formation of the material distribution. The method of Moving Asymptotes is used as an optimizer to update design variables in the optimization process. Several numerical examples are presented to evaluate the efficiency and reliability of the current approach.
  PubDate: 2023-03-17
Interdisciplinary design optimization of compressor blades combining low-
and high-fidelity models
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  Abstract: Abstract Multidisciplinary design optimization has great potential to support the turbomachinery development process by improving designs at reduced time and cost. As part of the industrial compressor design process, we seek for a rotor blade geometry that minimizes stresses without impairing the aerodynamic performance. However, the presence of structural mechanics, aerodynamics, and their interdisciplinary coupling poses challenges concerning computational effort and organizational integration. In order to reduce both computation times and the required exchange between disciplinary design teams, we propose an inter- instead of multidisciplinary design optimization approach tailored to the studied optimization problem. This involves a distinction between main and side discipline. The main discipline, structural mechanics, is computed by accurate high-fidelity finite element models. The side discipline, aerodynamics, is represented by efficient low-fidelity models, using Kriging and proper-orthogonal decomposition to approximate constraints and the gas load field as coupling variable. The proposed approach is shown to yield a valid blade design with reasonable computational effort for training the aerodynamic low-fidelity models and significantly reduced optimization times compared to a high-fidelity multidisciplinary design optimization. Especially for expensive side disciplines like aerodynamics, the multi-fidelity interdisciplinary design optimization has the potential to consider the effects of all involved disciplines at little additional cost and organizational complexity, while keeping the focus on the main discipline.
  PubDate: 2023-03-16
When is DiESL=ESL for linear dynamic response structural optimization'
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  Abstract: Abstract The Difference-based Equivalent Static Loads (DiESL) algorithm modifies the original ESL algorithm for nonlinear dynamic response structural optimization. The modifications in DiESL reportedly result in better approximations in the static response sub-problem and thus improved convergence properties of the algorithm. We study DiESL when applied to the special case of linear dynamic response structural optimization problems. Under certain assumptions, the two algorithms become identical in the sense that the static response sub-problems are equivalent.
  PubDate: 2023-03-16
A continuous model for connectivity constraints in topology optimization
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  Abstract: Abstract The aim of this work is to present a continuos mathematical model that characterizes and enforces connectivity in a topology optimization problem. That goal is accomplished by constraining the second eigenvalue of an auxiliary eigenproblem, solved together with the governing state law in each step of the iterative process. Our density-based approach is illustrated with 2d and 3d numerical examples in the context of structural design.
  PubDate: 2023-03-16
A new acquisition function combined with subset simulation for active
learning of small and time-dependent failure probability
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  Abstract: Abstract The time-dependent reliability analysis aims at estimating the probability of failure, occurring within a specified time period, of a structure subjected to stochastic and dynamic loads or stochastic degradation of performance. Development of efficient numerical algorithms with accuracy assurance for solving this problem, although has been investigated with, e.g., Gaussian Process Regression (GPR)-based active learning procedures, keeps being a bottleneck. Inspired by the concept of up-crossing rate used in the first-passage methods, a new acquisition function (also called learning function) is developed with the consideration of the temporal correlation information across each sample trajectory. It measures the (subjective) probability of mis-judging the occurrence of the up-crossing event within each time sub-interval. With this new acquisition function, the classical active learning procedure is improved. Considering the necessity for estimating small failure probability, the proposed active learning method is then combined with the subset simulation for multi-stage learning. With this method, a series of intermediate surrogate failure surface is actively updated with the target of approaching the true failure surface with pre-specified error tolerance. The effectiveness of the proposed methods are demonstrated with numerical and engineering examples.
  PubDate: 2023-03-16
Bi-directional evolutionary structural optimization with buckling
constraints
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  Abstract: Abstract Buckling is a critical phenomenon in structural members under compression, which could cause catastrophic failure of a structure. To increase the buckling resistance in structural design, a novel topology optimization approach based on the bi-directional evolutionary structural optimization (BESO) method is proposed in this study with the consideration of buckling constraints. The BESO method benefits from using only two discrete statuses (solid and void) for design variables, thereby alleviating numerical issues associated with pseudo buckling modes. The Kreisselmeier-Steinhauser aggregation function is introduced to aggregate multiple buckling constraints into a differentiable one. An augmented Lagrangian multiplier is developed to integrate buckling constraints into the objective function to ensure computational stability. Besides, a modified design variable update scheme is proposed to control the evolutionary rate after the target volume fraction is reached. Four topology optimization design examples are investigated to demonstrate the effectiveness of the buckling-constrained BESO method. The numerical results show that the developed optimization algorithm with buckling constraints can significantly improve structural stability with a slight increase in compliance.
  PubDate: 2023-03-16
Thermal design optimization method of mesh reflector antennas considering
the interaction between cable net and flexible truss
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  Abstract: Abstract Mesh antennas in orbit are periodically affected by solar radiation, earth reflection and space low temperature environment, and the temperature fluctuates in a wide range. Mesh antenna produce large thermal deformation or even obvious thermal disturbance under extreme temperature condition, which seriously deteriorates the surface accuracy and the tension distribution. To improve the shape stability of reflector surface and the rationality of tension distribution, a thermal design optimization method for mesh antenna considering the interaction between cable net and flexible truss is proposed. The equilibrium equation of mesh antenna system under space thermal loads is established based on finite element theory and force density equation. Due to the complexity of directly analyzing the influence of thermal loads on the entire mesh antenna, a research strategy of applying thermal loads step by step from flexible truss to cable network is adopted, and the force density increment equation of cable net under space thermal loads is derived. Then, the force density vector of the cable net is selected as the design variable, and the sum of squares of the thermal deformation of the reflector nodes is taken as the objective function, and the stability optimization model of the reflector in the whole temperature interval is established. Finally, a typical AstroMesh antenna under uniform temperature working conditions is used to illustrate the effectiveness and feasibility of the proposed method. Compared with the traditional optimization method, which can only ensure the better performance of a certain temperature point, the proposed method has better surface accuracy and thermal stability in the whole temperature interval.
  PubDate: 2023-03-16
Statistical prior modeling with radius-uniform distribution for a
correlation hyperparameter in bayesian calibration
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  Abstract: Abstract Model calibration is a process aimed at adjusting unknown parameters to minimize the error between the simulation model output and experimental observations. In computer-aided engineering, uncertainties in physical properties and modeling discrepancies can generate errors. Among various model calibration approaches, Kennedy and O’Hagan (KOH)’s Bayesian model calibration is noted for its ability to consider a variety of sources of uncertainty. However, one of the difficulties in KOH’s Bayesian model calibration is the complexity of determining the prior distributions of hyperparameters, which is often challenging in real-world problems due to insufficient information. Most previous studies have relied on users’ intuition to mitigate this issue. Thus, this study proposes a statistical prior modeling method for the correlation hyperparameter of a model discrepancy, which affects the calibration performance. In this work, a radius-uniform distribution is introduced as a prior distribution of the correlation hyperparameter based on the properties of the Gaussian process. Three case studies are provided, one numerical and two engineering cases, to confirm that the proposed method results in lower error than any other previously proposed distribution without additional computational cost. Further, the proposed method does not require user-dependent knowledge, which is a significant advantage over previous methods.
  PubDate: 2023-03-16
Form-finding design optimization method of cable mesh reflectors based on
a weighting surface accuracy with electromagnetic performance
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  Abstract: Abstract Form-finding design is a significant process for cable mesh reflectors to realize the required surface accuracy and electromagnetic performance. From the classification of the objective function, there are two kinds of optimization methods available for form-finding design: simple structural design optimization, which employs surface accuracy as the objective function, and integrated structural electromagnetic optimization, which directly utilizes the electromagnetic performance as the objective function. Although the electromagnetic performance can be reflected in integrated structural electromagnetic optimization, this necessitates complex computations and iterations. To solve these problems and inherit the advantages of multidisciplinary optimization, a weighting form-finding design optimization method is presented that chooses electromagnetic properties as the weighting coefficients to evaluate the surface accuracy and the weighting surface accuracy as the objective function. The proposed method can not only consider the electromagnetic properties, but also avoid complex computations and iterations. Compared with integrated structural electromagnetic optimization, the method can improve the iteration efficiency with satisfactory surface accuracy and electromagnetic performance. An offset cable mesh reflector and an umbrella cable mesh reflector are adopted to show the effectiveness and benefits of the proposed method.
  PubDate: 2023-03-07
Environmental and economical optimization of reinforced concrete overhang
bridge slabs
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  Abstract: Abstract The dimensioning of overhang slabs in bridge decks is usually based on simplified, thus conservative methods. The resulting over-dimensioned overhang bridge slabs can also affect the design of the girders. In this paper, an optimization procedure for the design of this structural element is presented. The aim is to minimize investment cost and global warming potential in the material production stage simultaneously while fulfilling all safety requirements. The design variables used in this study are the thicknesses of the overhang slab and the height of the edge beam. However, a complete detailed design of reinforcement is performed as well. Both a single-objective and a multi-objective formulation of the nonlinear problem are presented and handled with two well-known optimization algorithms: pattern search and genetic algorithm. The procedure is applied to a case study, which is a bridge in Sweden designed in 2013. One single solution minimizing both objective functions is found and leads to savings in investment cost and CO2-equivalent emissions of 4.2% and 9.3%, respectively. The optimization procedure is then applied to slab free lengths between 1 and 3 m. The outcome is a graph showing the optimal slab thicknesses for each slab length to be used by designers in the early design stage.
  PubDate: 2023-03-07
A radial-basis function mesh morphing and Bayesian optimization framework
for vehicle crashworthiness design
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  Abstract: Abstract The vehicular structural system design is critical to protect passengers from fatal injuries in inevitable accidents. Traditional optimization methods take only metal sheet thickness, i.e., thickness-based, as design variables due to the CAD re-modeling and re-meshing difficulties for changing the geometric shapes of assembled and interacted (welded, bolted, or riveted) parts inside the vehicle during an automatic optimization process. This, however, may limit the size of the design space and restrict the safety performance of the optimal design. In this study, a radial-basis function mesh morphing method is developed to change geometric shapes by moving node locations. Bayesian optimization is implemented to form a framework for handling the induced high-dimensional and nonlinear problem. A baseline model is validated and used as the initial design. Under the full-frontal crash scenario, four components selected based on the prior knowledge generated by a data mining method are parameterized by 32 variables, including node locations and metal sheet thickness. The node locations are constrained in case of the component intervention. Weighting vehicle peak acceleration and maximum intrusion of the passenger compartment form a single objective. Varying weights are responsible for generating the Pareto front. The results show that compared with the original design, the peak acceleration and maximum intrusion are reduced by 46.7 and 56.2%, respectively, at maximum. Structural bending modes and energy-absorbing behaviors are varied with different weights. Additional studies show that the node-based morphing method with a Bayesian optimization algorithm can achieve a better optimum globally than the traditional thickness-based method by a larger design space.
  PubDate: 2023-03-03