Ply level uncertainty effects on failure curves and optimal design of laminated composites using directional bat algorithm

The present study investigates the effect of both ply level material uncertainty and ply angle uncertainty on the failure envelope, strength characteristics and design of laminated composite. Multiple failure envelopes and distributions of the strength parameters are obtained for Tsai-Wu and maximum stress criteria using Monte Carlo simulation. A newly developed directional bat algorithm (dBA) is then used to perform the constrained design optimization of laminated composite for the first time while considering uncertainty effects. The effect of ply level uncertainty on failure envelopes and the corresponding optimal design of laminated composite structures is thus quantified.     

Hyperstatic and redundancy thresholds in truss topology optimization considering progressive collapse due to aleatory and epistemic uncertainties

Optimization leads to specialized structures which are not robust to disturbance events like unanticipated abnormal loading or human errors. Typical reliability-based and robust optimization mainly address objective aleatory uncertainties. To date, the impact of subjective epistemic uncertainties in optimal design has not been comprehensively investigated. In this paper, we use an independent parameter to investigate the effects of epistemic uncertainties in optimal design: the latent failure probability. Reliability-based and risk-based truss topology optimization are addressed. It is shown that optimal risk-based designs can be divided in three groups: (A) when epistemic uncertainty is small (in comparison to aleatory uncertainty), the optimal design is indifferent to it and yields isostatic structures; (B) when aleatory and epistemic uncertainties are relevant, optimal design is controlled by epistemic uncertainty and yields hyperstatic but nonredundant structures, for which expected costs of direct collapse are controlled; (C) when epistemic uncertainty becomes too large, the optimal design becomes redundant, as a way to control increasing expected costs of collapse. The three regions above are divided by hyperstatic and redundancy thresholds. The redundancy threshold is the point where the structure needs to become redundant so that its reliability becomes larger than the latent reliability of the simplest isostatic system. Simple truss topology optimization is considered herein, but the conclusions have immediate relevance to the optimal design of realistic structures subject to aleatory and epistemic uncertainties.     

Design optimization of composites using genetic algorithms and failure mechanism based failure criterion

In this paper, minimum weight design of composite laminates is presented using the failure mechanism based (FMB), maximum stress and Tsai–Wu failure criteria. The objective is to demonstrate the effectiveness of the newly proposed FMB failure criterion (FMBFC) in composite design. The FMBFC considers different failure mechanisms such as fiber breaks, matrix cracks, fiber compressive failure, and matrix crushing which are relevant for different loading conditions. A genetic algorithm is used for the optimization study. The Tsai–Wu failure criterion over predicts the weight of the laminate by up to 86% in the third quadrant of the failure envelope compared to FMB and maximum stress failure criteria, when the laminate is subjected to compressive–compressive loading. It is found that the FMB and maximum stress failure criteria give comparable weight estimates. The FMBFC can be considered for use in the strength design of composite structures.     

Dual-mode nested search method for categorical uncertain multi-objective optimization

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.     

基于遗传算法的复合材料层合板削层结构铺层优化

针对应力变化较大的碳纤维增强复合材料层合板,提出削层结构铺层分级优化模式。通过将结构分解为若干子铺层并对各子铺层的位置、尺寸、铺层数以及铺层顺序进行优化,得到了满足强度和可制造性要求且质量最小的结构设计方案。该模式的第1、2级优化利用参考层对各子铺层位置及尺寸进行优化,第3级优化通过引入3次样条插值参数化方法对各子铺层层数和铺层顺序进行优化。参考层的引入可减少设计变量的数量,3次样条插值参数化方法可解决以铺层角为设计变量时设计变量数目不确定的问题。利用有限元方法对结构进行力学分析计算,并依据Tsai-Wu准则确定结构强度。在第2、3级优化中利用遗传算法对优化问题进行求解。算例计算表明:削层结构铺层分级优化模式结果合理可信。与均匀铺层方法结果比较可知:削层结构可有效减少结构质量。     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

Fault-tolerant embedded system design and optimization considering reliability estimation uncertainty

In this paper, we model embedded system design and optimization, considering component redundancy and uncertainty in the component reliability estimates. The systems being studied consist of software embedded in associated hardware components. Very often, component reliability values are not known exactly. Therefore, for reliability analysis studies and system optimization, it is meaningful to consider component reliability estimates as random variables with associated estimation uncertainty. In this new research, the system design process is formulated as a multiple-objective optimization problem to maximize an estimate of system reliability, and also, to minimize the variance of the reliability estimate. The two objectives are combined by penalizing the variance for prospective solutions. The two most common fault-tolerant embedded system architectures, N-Version Programming and Recovery Block, are considered as strategies to improve system reliability by providing system redundancy. Four distinct models are presented to demonstrate the proposed optimization techniques with or without redundancy. For many design problems, multiple functionally equivalent software versions have failure correlation even if they have been independently developed. The failure correlation may result from faults in the software specification, faults from a voting algorithm, and/or related faults from any two software versions. Our approach considers this correlation in formulating practical optimization models. Genetic algorithms with a dynamic penalty function are applied in solving this optimization problem, and reasonable and interesting results are obtained and discussed.     

基于可靠性的复合材料定向管优化设计

基于Tsai-Wu失效准则和一次二阶矩法,建立了复合材料定向管强度可靠性分析的方法。应用Python语言实现了ABAQUS 的二次开发,编程将有限元计算程序与可靠性分析方法相结合,并采用多岛遗传算法和序列二次规划算法相结合优化策略,建立了基于可靠性的定向管铺层参数动态优化模型。优化算例表明:在满足强度可靠度条件下,复合材料定向管重量减小了22.5%。     

Bearing Failure Optimization of Composite Double-Lap Bolted Joints Based on a Three-Step Strategy Marked By Feasible Region Reduction and Model Decoupling

To minimize the mass and increase the bearing failure load of composite doublelap bolted joints, a three-step optimization strategy including feasible region reduction, optimization model decoupling and optimization was presented. In feasible region reduction, the dimensions of the feasible design region were reduced by selecting dominant design variables from numerous multilevel parameters by sensitivity analyses, and the feasible regions of variables were reduced by influence mechanism analyses. In model decoupling, the optimization model with a large number of variables was divided into various sub-models with fewer variables by variance analysis. In the third step, the optimization sub-models were solved one by one using a genetic algorithm, and the modified characteristic curve method was adopted as the failure prediction method. Based on the proposed optimization method, optimization of a double-lap single-bolt joint was performed using the ANSYS^® code. The results show that the bearing failure load increased by 13.5% and that the mass decreased by 8.7% compared with those of the initial design of the joint, which validated the effectiveness of the three-step optimization strategy.     

Condition‐based Maintenance Optimization Using Neural Network‐based Health Condition Prediction

Artificial neural network (ANN)‐based methods have been extensively investigated for equipment health condition prediction. However, effective condition‐based maintenance (CBM) optimization methods utilizing ANN prediction information are currently not available due to two key challenges: (i) ANN prediction models typically only give a single remaining life prediction value, and it is hard to quantify the uncertainty associated with the predicted value; (ii) simulation methods are generally used for evaluating the cost of the CBM policies, while more accurate and efficient numerical methods are not available, which is critical for performing CBM optimization. In this paper, we propose a CBM optimization approach based on ANN remaining life prediction information, in which the above‐mentioned key challenges are addressed. The CBM policy is defined by a failure probability threshold value. The remaining life prediction uncertainty is estimated based on ANN lifetime prediction errors on the test set during the ANN training and testing processes. A numerical method is developed to evaluate the cost of the proposed CBM policy more accurately and efficiently. Optimization can be performed to find the optimal failure probability threshold value corresponding to the lowest maintenance cost. The effectiveness of the proposed CBM approach is demonstrated using two simulated degradation data sets and a real‐world condition monitoring data set collected from pump bearings. The proposed approach is also compared with benchmark maintenance policies and is found to outperform the benchmark policies. The proposed CBM approach can also be adapted to utilize information obtained using other prognostics methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of copper filled fibreglass moulds for manufacturing a customized product using linear programming optimization and finite element analysis

This paper presents a design procedure and cost analysis for a mould made of glass fibre reinforced polyester filled with copper particles (GRP/copper). It also describes their potential use in rotational moulding as an alternative to steel and aluminium moulds operating at high temperatures up to 250 °C. The thermal conductivity of glass reinforced polyester (GRP) was improved by incorporating copper particles acting as fillers in the composite. An optimum composite structure consisting of 25% glass fibres, 45% polyester, and 30% copper was achieved by linear programming search optimization methods. Then a finite element analysis (FEA) of a typical GRP/copper mould made of the optimized composite structure under thermal loading was conducted. The induced thermal stresses obtained from FEA were used to check the failure condition of the mould using the Tsai–Hill failure criterion. The FEA design procedure was also used to determine the mould thickness with a safety factor of at least four. Scheduling and cost analysis showed that 76% reduction in production time and 64% reduction in manufacturing costs have been achieved with the developed method.     

OPTIMUM DESIGN OF LAMINATED COMPOSITE STRUCTURES VIA AMULTILEVEL SUBSTRUCTURING APPROACH

This paper presents a multilevel substructuring and optimization approach to the minimum weight design of laminated composite structures. The optimization process is carried out in a double scheme which consists of optimizations at system and subsystem levels. At the system level of optimization, an optimality criterion method is used to design component thicknesses which minimize structural weight subject to structural behavioral constraints as well as side constraints. At the subsystem level, the structure being divided into several substructures, fiber directions and layer thicknesses of each substructure are determined to minimize its weight subject to component behavioral constraints as well as side constraints. The objective at the subsystem level is accomplished by carrying out the minimization process again in a double scheme where the quasi-Newton method is used at the first sub-level of optimization for the optimal design of fiber directions and an optimality criterion method at the second sub-level for layer thickness design. The optimal solution is obtained by iterating between the different levels of optimization. Appropriate connectivity conditions for linking different levels of optimization are introduced to ensure convergence of solution. The feasibility and application of the present approach is illustrated by an example of the optimal design of a single-cell, three bay, cantilevered boxbeam.     

Generalized information reuse for optimization under uncertainty with non‐sample average estimators

In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multifidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multifidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multifidelity method that treats previous optimization iterations as lower fidelity models. This work generalizes information reuse to be applicable to quantities whose estimators are not sample averages. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared with regular Monte Carlo sampling.     

A new interval optimization method considering tolerance design

This study considers the design variable uncertainty in the actual manufacturing process for a product or structure and proposes a new interval optimization method based on tolerance design, which can provide not only an optimal design but also the allowable maximal manufacturing errors that the design can bear. The design variables' manufacturing errors are depicted using the interval method, and an interval optimization model for the structure is constructed. A dimensionless design tolerance index is defined to describe the overall uncertainty of all design variables, and by combining the nominal objective function, a deterministic two-objective optimization model is built. The possibility degree of interval is used to represent the reliability of the constraints under uncertainty, through which the model is transformed to a deterministic optimization problem. Three numerical examples are investigated to verify the effectiveness of the present method.     

不确定视角下产品结构性能优化设计综述与展望

目的 复杂产品在工程装备、航空航天等我国优先发展的战略领域中扮演着不可替代的重要角色,在其结构设计过程中普遍存在着各种不确定性,导致产品结构性能很难实现最优,甚至出现重大故障。方法 针对复杂产品设计过程中的多粒度模糊不确定、随机不确定、不完备区间不确定和高维混合不确定等特点,将不确定性理论与产品结构设计过程相结合,系统地构建了不确定视角下产品结构性能优化设计理论体系,提出了多粒度模糊不确定下产品质量特性精准提取、随机不确定下产品功能结构模块化求解、不完备区间不确定下产品结构方案多属性决策、高维混合不确定下产品关键结构可靠性优化等关键技术,并指出了产品结构性能优化设计的未来发展方向。结论 此设计理论能够充分适应和利用产品设计过程的多种不确定信息,为在结构设计环节切实提升产品性能提供了有力参考。     

激光精跟踪快速控制反射镜结构优化与分析

目的对快速控制反射镜进行结构优化与处理,获得满足设计要求的轻量化结构。方法选取合适的加工材料,建立以结构柔度最小为目标的优化数学模型进行拓扑优化,对优化后提取的结构模型进行处理和有限元仿真分析。结果通过优化与分析,确定了反射镜最终结构,模拟分析结果表明,镜面最大变形量为2.7 nm,基频为4130.3 Hz,均满足设计要求。优化前后相比,结构质量降低了57.8%。结论优化结果较好满足了设计要求,对于类似结构的设计具有一定的参考作用。     

Optimization of structures under material parameter uncertainty using evidence theory

An evidence-based approach is developed for optimization of structural components under material parameter uncertainty. The approach is applied to evidence-based design optimization (EBDO) of externally stiffened circular tubes under axial impact load using an isotropic–elastic–plastic plasticity model to simulate dynamic material behaviour. Uncertainty modelling considers the changes in material parameters that are caused by variability in material properties as well as incertitude and errors in experimental data and procedure to determine the material parameters. Spatial variation of material parameters across the structural component is modelled using a field joint belief structure and propagated for the calculation of evidence-based objective function and design constraints. Surrogate models are used in both uncertainty propagation and solution of the optimization problem. The methodology and the solution to the EBDO example problem are presented and discussed.     

Adaptive gradient-assisted robust design optimization under interval uncertainty

Robust optimization techniques attempt to find a solution that is both optimum and relatively insensitive to input uncertainty. In general, these techniques are computationally more expensive than their deterministic counterparts. In this article two new robust optimization methods are presented. The first method is called gradient-assisted robust optimization (GARO). In GARO, a robust optimization problem is first converted to a deterministic one by using a gradient-based approximation technique. After solving this deterministic problem, the solution robustness and the accuracy of the approximation are checked. If the accuracy meets a threshold, a robust optimum solution is found; otherwise, the approximation is adaptively modified until the threshold is met and a solution, if it exists, is obtained. The second method is a faster version of GARO called quasi-concave gradient-assisted robust optimization (QC-GARO). QC-GARO is for problems with quasi-concave objective and constraint functions. The difference between GARO and QC-GARO is in the way that they check the approximation accuracy. Both GARO and QC-GARO methods are applied to a set of six engineering design test problems and the results are compared with a few related previous methods. It was found that, compared to the methods considered, GARO could solve all test problems but with a higher computational effort compared to QC-GARO. However, QC-GARO was computationally much faster when it was able to solve the problems.     

Reliability based design optimization using response surfaces in application to multidisciplinary systems

Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state functions are used to estimate the probability of failure. An outer loop is incorporated to ensure that the approximate RBDO converges to the actual most probable point of failure. The framework is compared with the exact RBDO procedure. In the proposed methodology, RSAs are employed to significantly reduce the computational expense associated with traditional RBDO. The proposed approach is implemented in application to multidisciplinary test problems, and the computational savings and benefits are discussed.     

Optimal design and control of a reactive distillation system

This article presents the design and control of a reactive distillation system utilizing recent advances in mixed integer dynamic optimization. A high fidelity dynamic model is used to predict the behavior of the process under time-varying disturbances. Design and control decisions, involving both discrete and continuous variables, are simultaneously optimized leading to a more economically attractive and better controlled system than that obtained by following a sequential optimization approach. It is shown that the resulting design and control scheme can guarantee feasible operation under bounded uncertainty at a minimum total average cost, representing ～17% savings over the original design.