Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model

Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.     

An efficient truss structure optimization framework based on CAD/CAE integration and sequential radial basis function metamodel

In order to improve the performance and efficiency of truss structure optimization, this paper presents a general framework that embeds and seamlessly integrates commercial CAD and CAE software through common programming languages and application programming interface (API). Along with the automatic CAD/CAE integration, an adaptive metamodel-based optimization called sequential radial basis function (SRBF) is applied to truss structure optimization involving sizing, geometry and topology variables. SRBF distinguishingly features two-loops searching strategy, the “inner loop” and the “outer loop”. The “inner loop” aims to search a feasible point through updating the factors of the augmented Lagrangian function. With the improved significant sampling space (ISSS) method, the “outer loop” sequentially generates new additional samples to update the RBF model. The continuous relaxation method is developed to deal with the mixed-discrete variables during the truss structure optimization. Applied to practical truss structure optimization problems from small scale to large scale, the proposed framework demonstrates feasibility of the CAD/CAE integration system during the structure modeling and analysis, and facilitates the truss structure optimization process. The comparison results between the SRBF and other approaches show that SRBF improves merit of searching global optimum and reduces the computation cost.     

On design optimization for structural crashworthiness and its state of the art

Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption.

     

Isogeometric topology optimization using trimmed spline surfaces

In the present work, a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed. In the proposed approach, the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by CAD systems is employed for structural response analysis and sensitivity calculation in the topology optimization. The outer and inner boundaries of design models are represented by a spline surface and trimming curves. Design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves. New sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified. The creation of new inner fronts during optimization is allowed for the topological flexibility. An inner front merging algorithm is also presented. The proposed spline based topology optimization is used to solve some benchmarking problems. Design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization. Design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one. It is also shown that post-processing effort for converting to CAD model is eliminated by using the same spline information in numerical analysis and design optimization.     

Structural design and global sensitivity analysis of the composite B-pillar with ply drop-off

Vehicle lightweight and safety design becomes an increasingly critical issue nowadays. In order to improve the crashworthiness of side impact and roof crush with the consideration of the manufacturing process, a new composite B-pillar structure with ply drop-off is proposed in this paper. It improves the crashworthiness by changing the section thickness of structure and reduces the weight of B-pillar. The ply drop-off regions on the outer part and inner part of B-pillar are divided into three sub-laminates respectively, named as thick panel, taper panel and thin panel. The thickness of the panel are determined by the number of lay-up. Based on traditional sensitivity analysis, this paper derives some new equations and clearly evaluates and quantifies the importance of uncertainty design parameters. Finally, the comprehensive performance of the lightweight and crashworthiness for the composite B-pillar with ply drop-off is improved through structural optimization.     

考虑自动驾驶仪动态特性的三维双环制导律

针对导弹自动驾驶仪动态特性条件下的机动目标拦截问题,基于非线性干扰观测器和命令滤波器设计一种新的三维双环制导律.将制导系统解耦为外环系统和内环系统.其中:外环控制器产生虚拟制导指令,以零化球坐标系下的弹目法向相对速率;内环控制器产生真实制导指令,以实现导弹自动驾驶仪对外环虚拟指令的快速跟踪.由于外环命令滤波器同时计算出虚拟制导指令的一阶导数和二阶导数,三阶系统的制导律设计问题仅用两步即可完成.拦截高速高机动目标的仿真结果表明,所设计的制导律能够有效补偿导弹自动驾驶仪动态特性影响,抗目标机动鲁棒性强,制导精度优良.     

An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers

Analytical target cascading is a method for design optimization of hierarchical, multilevel systems. A quadratic penalty relaxation of the system consistency constraints is used to ensure subproblem feasibility. A typical nested solution strategy consists of inner and outer loops. In the inner loop, the coupled subproblems are solved iteratively with fixed penalty weights. After convergence of the inner loop, the outer loop updates the penalty weights. The article presents an augmented Lagrangian relaxation that reduces the computational cost associated with ill-conditioning of subproblems in the inner loop. The alternating direction method of multipliers is used to update penalty parameters after a single inner loop iteration, so that subproblems need to be solved only once. Experiments with four examples show that computational costs are decreased by orders of magnitude ranging between 10 and 1000.     

基于响应面法的汽车前防撞梁轻量化分析

将原来的汽车前防撞横梁材料替换成超高强度钢后,在确保低速碰撞性能基础上,利用响应面法进行轻量化分析.建立前防撞梁有限元模型,用LS-DYNA进行低速碰撞仿真.在此基础上以横梁和吸能盒的厚度作为变量进行试验设计.构建各项碰撞性能的2阶多项式响应面模型,并验证模型的有效性.以质量和吸能作为优化目标,建立多目标优化模型.与原设计相比,求出的优化方案在保证低速碰撞性能的基础上实现前防撞梁减重36%.     

Component and system reliability-based topology optimization using a single-loop method

We perform reliability-based topology optimization by combining reliability analysis and material distribution topology design methods to design linear elastic structures subject to random inputs, such as random loadings. Both component reliability and system reliability are considered. In component reliability, we satisfy numerous probabilistic constraints which quantify the failure of different events. In system reliability, we satisfy a single probabilistic constraint which encompasses the component events. We adopt the first-order reliability method to approximate the component reliabilities and the inclusion-exclusion rule to approximate the system reliability. To solve the probabilistic optimization problem, we use a variant of the single loop method, which eliminates the need for an inner reliability analysis loop. The proposed method is amenable to implementation with existing deterministic topology optimization software, and hence suitable for practical applications. Designs obtained from component and system reliability-based topology optimization are compared to those obtained from traditional deterministic topology optimization and validated via Monte Carlo simulation.     

A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization

We present a new hybrid method for solving constrained numerical and engineering optimization problems in this paper. The proposed hybrid method takes advantage of the differential evolution (DE) ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using a modified augmented Lagrangian multiplier method. The basic steps of the proposed method are comprised of an outer iteration, in which the Lagrangian multipliers and various penalty parameters are updated using a first-order update scheme, and an inner iteration, in which a nonlinear optimization of the modified augmented Lagrangian function with simple bound constraints is implemented by a modified differential evolution algorithm. Experimental results based on several well-known constrained numerical and engineering optimization problems demonstrate that the proposed method shows better performance in comparison to the state-of-the-art algorithms.     

Integrated design technique for materials and structures of vehicle body under crash safety considerations

With the rapid development of the vehicle industry, crashworthiness has become a crucial aspect in vehicle body design. In fact, crashworthiness is a multivariable optimization design problem for a vehicle body, regardless of structure or material. However, when crashworthiness involves a large number of design variables, including both material and structure variables, it is more difficult to deal with. In this paper, an integrated design technique for materials and structures of vehicle body under crash safety consideration is suggested. First, a finite element model of the vehicle body is established according to relevant vehicle safety standards. Then, the material parameters of the vehicle body are set as analytical factors for factor screening. Next, significant factors are obtained using a three-level saturated design integrated with multi-index comprehensive balance analysis and the MaxUr ⁽³⁾ method, with an improved evaluation method. These screened material parameters along with the corresponding continuous variables of the structure, are considered as the design variables of the integrated design of the vehicle body. Both the weight and the crashworthiness properties are set as the design objectives. Optimal Latin hypercube sampling and radius basis functions are utilized to construct highly accurate surrogate models. Furthermore, the non-dominated sorting genetic algorithm II is implemented to seek the optimal solutions. Finally, two cases considering the roof module and the frontal module of a vehicle body are analyzed to verify the proposed method.     

Design of materials using hybrid cellular automata

This paper presents a new approach for the topological design of materials with extreme properties. The method is based on hybrid cellular automaton (HCA), which is an implicit optimization technique that uses local rules to update design variables iteratively until meeting the described optimality conditions. By means of an energy-based homogenization approach, the effective properties of the considered material are calculated in terms of element mutual energies. By this method, no sensitivity information is required to find the optimal topology for the considered design objectives: bulk modulus, shear modulus, and negative Poisson’s ratio. The proposed method is validated by a series of numerical examples.     

Two approaches for solving the buffer allocation problem in unreliable production lines

This paper presents an integrated approach to solve the buffer allocation problem in unreliable production lines so as to maximize the throughput rate of the line with minimum total buffer size. The proposed integrated approach has two control loops; the inner loop and the outer loop. While the inner loop control includes an adaptive tabu search algorithm proposed by Demir et al. [8], binary search and tabu search are proposed for the outer loop. These nested loops aim at minimizing the total buffer size to achieve the desired throughput level. To improve the efficiency of the proposed tabu search, alternative neighborhood generation mechanisms are developed. The performances of the proposed algorithms are evaluated by extensive computational experimentation, and the results are reported.     

Robust optimization with convex model considering bounded constraints on performance variation

In robust optimization, double-looped structures are often adopted where the outer loop is used to seek for the optimal design and the optimization performed in the inner loop is for the robustness assessment of the candidate solutions. However, the double-looped techniques usually will lead to a significant increase in computational efforts. Therefore, in this paper, a new robustness index is developed to handle bounded constraints on performance variation where no optimization run is required for the robustness evaluation work in the inner loop. The computation of this new index is based on the sensitivity Jacobian matrix of the system performances with respect to the uncertainties and it can quantitatively measure the maximal allowable magnitude of system variations. By introducing this index, the robust design problem can be reformulated as a deterministic optimization with robustness indices requirements. Two numerical examples are tested to show the effectiveness and efficiency of the proposed approach, whose solutions and computational efforts are compared to those from a double-looped approach proposed in previous literature.     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

A sharp augmented Lagrangian-based method in constrained non-convex optimization

In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

Uniform crashworthiness optimization of car body for high-speed trains

The paper deals with a new uniform crashworthiness concept of car bodies optimization of high-speed trains. The design optimization was done from the point of view of structural protection of occupants’ survival space. For the reason that it is impossible to find a highly probable scenario for the derailment, the authors decided to find the solution in the form of rigid frame structure (survival cells), which will provide safety space for the passengers. In the optimization example a typical passenger car body was divided into cells of approximately equal dimensions. The optimization problem was to minimize the mass of the structure with stress constraints. The survival cell was subjected to a sequence of high value loads. The loads are acting in an asynchronous way in three load directions what gives the optimized structure uniform crashworthiness. The optimization strategy consists of three stages. In the first step, the constant criterion surface algorithm (CCSA) of topology optimization is applied to find a preliminary solutions. For improving the manufacture properties of this solution, a new concept of design space constraints was proposed. The sizing optimization with evolutionary algorithms was used to define a thin-walled structure in the second step. For evolutionary optimization a standard procedure was employed. Finally, CCSA optimization algorithm was applied again to remove excessive material from a car body structure. As the optimization result a new design proposition of a car body with multiple survival cells of high uniform stiffness was obtained. By maintaining passengers’ survival space, the passive safety of a high-speed car body was significantly increased.     

Structural optimization with crashworthiness constraints

An automated structural design methodology has been devised which simultaneously considers design criteria associated with both linear elastic and crashworthiness loading conditions. This method is developed within the context of a nonlinear mathematical programming based structural optimization capability using an efficient two-phased crashworthiness analysis technique. Specially constructed nonlinear approximations for the crashworthiness constraints are employed to further reduce the computational burden during the optimization process. This methodology is demonstrated on an automobile structural design problem. It is shown that more mass efficient designs can be obtained by simultaneously considering elastic and crashworthiness design criteria as compared to a sequential approach in which the structure is first designed for the elastic loads and then modified to satisfy the crashworthiness criteria.     

基于平动转动分离的车道线双回路滑模控制研究

针对车辆自主驾驶中的车道线保持问题,基于车辆横向动力学简化线性模型,把车辆运动分为平动与转动,按照平动与转动分离的思想,采用内外回路分层设计的方法,提出了一类以角度稳定为内稳定核心回路,以位置误差跟踪为外回路的双回路控制方案.其内外回路相串联,并由车辆平动位置信息驱动转动角稳定回路,对双回路均采用滑模控制方法.最后,采用详细的仿真分析说明了该设计方法具有明确的物理意义,而且控制律构成不包含系统不确定信息,具有很好的鲁棒性,能够满足工程应用的需要.