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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Abstract: Abstract This paper presents a CAD-aware plug-and-play framework for topology optimization that results in CAD compatible-optimized geometries. The framework uses two separate kernels: one for defining and updating the geometry, and the other for an unfitted finite element analysis (FEA). The level-set method is used for the handling the geometry, while a moment-vector based simulation is used for the FEA. Moments can be used to generate quadrature rules for arbitrary geometries, which in turn can be used to accurately compute finite element entities such as stiffness or mass matrices. We introduce the notion of moment-averaged stress that can accurately capture maximum stress without post-processing or stress reconstruction. We also present the adjoint sensitivity analysis that enables the moment-based simulation to be coupled with the level-set method. Using numerical examples in 2D and 3D, we show the efficiency of our method in producing lightweight designs optimized for minimum compliance and minimum stress. More importantly, we show that the framework allows for the optimized geometry to be seamlessly exported as CAD compatible formats without the need for any cumbersome post-processing. PubDate: 2023-02-28
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Abstract: Abstract To reduce the computational cost, multi-fidelity (MF) metamodel methods have been widely used in engineering optimization. Most of these methods are based on the standard Gaussian random process theory; thus, the time cost required for hyperparameter estimation increases significantly with an increase in the dimension and nonlinearity of the problems especially for high-dimensional problems. To address these issues, by exploiting the great potential of deep neural networks in high-dimensional information extraction and approximation, a meta-learning-based multi-fidelity Bayesian neural network (ML-MFBNN) method is developed in this study. Based on this, to further reduce the computational cost, an adaptive multi-fidelity sampling strategy is proposed in combination with Bayesian deep learning to sequentially select the highly cost-effective samples. The effectiveness and advantages of the proposed MF-MFBNN and adaptive multi-fidelity sampling strategy are verified through eight mathematical examples, and the application to model validation of computational fluid dynamics and robust shape optimization of the ONERA M6 wing. PubDate: 2023-02-28
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Abstract: Abstract Statistical analysis is frequently used to determine how manufacturing tolerances or operating condition uncertainties affect system performance. Surrogate is one of the accelerating ways in engineering tolerance quantification to analyze uncertainty with an acceptable computational burden rather than costly traditional methods such as Monte Carlo simulation. Compared with more complicated surrogates such as the Gaussian process, or Radial Basis Function (RBF), the Polynomial Regression (PR) provides simpler formulations yet acceptable outcomes. However, PR with the common least-squares method needs to be more accurate and flexible for approximating nonlinear and nonconvex models. In this study, a new approach is proposed to enhance the accuracy and approximation power of PR in dealing with uncertainty quantification in engineering tolerances. For this purpose, first, by computing the differences between training sample points and a reference point (e.g., nominal design), we employ certain linear and exponential basis functions to transform an original variable design into new transformed variables. A second adjustment is made to calculate the bias between the true simulation model and the surrogate’s approximated response. To demonstrate the effectiveness of the proposed PR approach, we provide comparison results between conventional and proposed surrogates employing four practical problems with geometric fabrication tolerances such as three-bar truss design, welded beam design, and trajectory planning of two-link and three-link (two and three degrees of freedom) robot manipulator. The obtained results prove the preference of the proposed approach over conventional PR by improving the approximation accuracy of the model with significantly lower prediction errors. PubDate: 2023-02-28
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Abstract: Abstract Accurate assessment of the remaining life of infrastructure assets is important for safe operation and efficient maintenance. In the case of inland navigation infrastructure, the United States Army Corps of Engineers have identified the embedded steel anchorages on miter gates as a critical component of the infrastructure network. Many of these anchorages are of an age such that they are at or beyond their useful life. The embedded nature of the anchorage precludes visual inspection, and the complicated interaction between the steel anchorage components and the embedding concrete is challenging to analyze. The traditional analysis method of the anchorages neglects the concrete embedment when determining member stresses. As a result, a conservative estimate of remaining fatigue life is obtained. A more accurate assessment of member stresses has shown that the surrounding concrete significantly reduces the steel stresses, resulting in substantially longer estimates of remaining life. To generalize results obtained from tests of a specific miter gate specimen to be more broadly applicable to other embedded anchorages, this work uses Bayesian model updating to calibrate a set of springs representative of the concrete embedment. These spring constants can be used in the analysis of other embedded anchorage configurations to obtain a more accurate assessments of remaining fatigue life. PubDate: 2023-02-28
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Abstract: Abstract This paper presents a new topology optimization framework in which the design decisions are made by humans and machines in collaboration. The new Human-Informed Topology Optimization approach eases the accessibility of topology optimization tools and enables improved design identification for the so-called ‘everyday’ and ‘in-the-field’ design situations. The new framework is based on standard density-based compliance minimization. However, the design engineer is enabled to actively use their experience and expertise to locally alter the minimum feature size requirements. This is done by conducting a short initial solution and prompting the design engineer to evaluate the quality. The user can identify potential areas of concern based on the initial material distribution. In these areas, the minimum feature size requirement can be altered as deemed necessary by the user. The algorithm rigorously resolves the compliance problem using the updated filtering map, resulting in solutions that eliminate, merge, or thicken topological members of concern. The new framework is demonstrated on 2D benchmark examples and the extension to 3D is shown. Its ability to achieve performance improvement with few computational resources are demonstrated on buckling and stress concentration examples. PubDate: 2023-02-28
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Abstract: Abstract Channel cooling structures are widely used in heat generating products and tools. A popular combination has been designing using the topology optimization method and manufacturing by an advanced method, such as 3D printing. Considering the heat sink design with its thermal mechanical effects, a feature-based cooling channel topology optimization design method is given. The presented method is adopted to accurately describe the topological parameters in the cooling channel structure. To address the phenomenon of mixing between different phases and avoid the parameter continuation tuning process by using the feature-based method, a phase-mixing constraint is proposed. To improve the computational efficiency, an equivalent flow field model fit to low and high Reynold’s number is proposed. The shape feature parameters are discussed in more detail. Furthermore, a hot stamping tool is taken as an example, in which the topology optimization design of the cooling channel structure is carried out and discussed. PubDate: 2023-02-28
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Abstract: Abstract The vehicle structure is a highly complex system as it is subject to different requirements of many engineering disciplines. Multidisciplinary optimization (MDO) is a simulation-based approach for capturing this complexity and achieving the best possible compromise by integrating all relevant CAE-based disciplines. However, to enable operative application of MDO even under consideration of crash, various adjustments to reduce the high numerical resource requirements and to integrate all disciplines in a target way must be carried out. They can be grouped as follows: The use of efficient optimization strategies, the identification of relevant load cases and sensitive variables as well as the reduction of CAE calculation time of costly crash load cases by so-called finite element (FE) submodels. By assembling these components in a clever way, a novel, adaptively controllable MDO process based on metamodels is developed. There are essentially three special features presented within the scope of this paper: First, a module named global sensitivity matrix which helps with targeted planning and implementation of a MDO by structuring the multitude of variables and disciplines. Second, a local, heuristic and thus on all metamodel types computable prediction uncertainty measure that is further used in the definition of the optimization problem. And third, a module called adaptive complexity control which progressively reduces the complexity and dimensionality of the optimization problem. The reduction of resource requirements and the increase in the quality of results are significant, compared to the standard MDO procedure. This statement is confirmed by providing results for a FE full vehicle example in six load cases (five crash load cases and one frequency analysis). PubDate: 2023-02-28
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