基于可靠度的结构优化的序列近似规划算法

基于可靠度的优化的最直观解法是把可靠度和优化的各自算法搭配一起形成嵌套两层次迭代。为改善其收敛性提高计算效率,人们提出了功能测度法、半无限规划法、单层次算法等多种改进方法。本文对传统结构优化界的经典序列近似规划法改造并扩展应用于求解基于可靠度的结构优化问题,构造该问题的序列近似规划模型和求解过程;其核心思想是在每个近似规划子问题中采用近似可靠度指标对设计变量的线性近似,在优化迭代过程中同步更新设计变量和随机空间中的近似验算点坐标,以达到可靠度分析和优化迭代同步收敛的目标。为了算法的实施,还推导出近似可靠度指标的半解析灵敏度计算公式,编制了程序,最终实现与通用软件的连接。论文用算例证实算法的有效性。     

声场-结构耦合系统声压约束下板重量优化设计研究

为了减小振动板重量并使其振动噪声满足设计要求,基于声场-结构耦合有限元模型,提出了使结构重量最小化、满足声压约束的优化设计模型。用有限元直接法计算耦合系统的声响应及域点声压对结构设计变量的灵敏度,用可行方向法对其进行了优化设计研究。以一矩形平板和立方体声场耦合系统为实例,以壳厚度为设计变量,给出了域点声压对结构设计变量的灵敏度、优化前和优化后声压级对比图及最优的设计变量值。经过优化设计,在1Hz~200Hz频段内域点声压最大值降低6分贝,结构重量减少1.88千克。结果表明,声压约束下结构重量最小化设计,通过对结构重量的重新分布,能同时满足结构轻量化及噪声指标的要求。     

多变量单元结构共振解耦动力优化设计方法

针对截面多变量单元结构的动力优化问题，建立了带频率约束的结构动力优化设计模型，对隐式非线性频率约束函数进行Taylor近似展开，给出了截面多变量单元频率梯度函数显式表达式，基于Kuhn-Tucker条件构建迭代算法，其中拉格朗日乘子通过建立联合方程组求解，形成了含多变量单元共振解耦优化设计方法。以矩形截面单元结构为算例的结果表明，所给单元多变量算法具有良好的准确性；截面变量对频率的贡献存在主次之分，区分指标可采用梯度值；次要变量的修正因子迭代中可采用定值，且其下限应尽可能降低，利于节约成本。本文工作对多变量复杂截面结构动力优化设计可提供理论指导，提高结构动力优化方法的适用性。     

带不确定混合噪声系统的变分贝叶斯期望最大滤波算法

卡尔曼滤波器假设量测噪声为已知统计特性的高斯白噪声,然而系统可能受到不确定随机噪声以及未知有界噪声共同影响,若采用单一滤波策略,则估计结果易出现较大偏差。将两种不确定噪声运用未知参数的高斯混合模型进行表示,提出变分贝叶斯期望最大滤波算法。所提方法采用变分贝叶斯最大化方法对量测噪声模型中的超参数进行更新,在得到模型超参数后,利用变分贝叶斯期望算法计算噪声模型的隐变量。对上述过程反复迭代,最终获得系统的状态和协方差。仿真结果表明,相比于传统的卡尔曼滤波算法和联合滤波算法,变分贝叶斯期望最大滤波算法在出现混合不确定噪声时,经纬度定位精度均提高60%以上,提高了导航系统的精确性。     

频率约束板结构拓扑优化

本文利用ICM（独立、连续、映射）方法建立了频率约束下平板结构重量最轻的拓扑优化模型。采用指数函数作为单元重量、单元质量及单元刚度的过滤函数。通过瑞利商对刚度过滤函数倒变量的泰勒一阶展式,将频率约束近似显式化。利用对偶理论将含有大量设计变量的约束优化模型转化为易于求解的少设计变量拟无约束优化模型,通过序列二次规划将转化模型进行求解,提高了求解的效率。本文选择MSC.Patran&Nastran软件及PCL二次开发语言构架了平板结构频率约束拓扑优化问题的软件。数值算例表明：本文的方法具有迭代稳定性和收敛高效性。     

不同路面激励下车内噪声预测与板件声学贡献量分析

利用有限元模拟计算的方法对不同路面激励下车内噪声进行了预测, 并分析了板件对声 学的贡献量. 使用MATLAB软件生成了B级和C级路面谱. 由NASTRAN软件计算 出车身结构在不同路面谱激励下1$\sim$200\,Hz的频率响应结果, 在LMS Virtual. Lab声学软件中, 根据声传递向量技术预测驾驶员和乘客耳旁声压级响应. 还探讨了 声腔结构表面阻抗特性对车内噪声的影响. 并针对C级路面谱激励, 通过车身各板件对 驾驶员右耳声压的面板贡献量分析, 找出了结构优化的重点区域, 为降低车内声压检测点噪 声进行相关的声学处理提供参考依据.     

结构可靠度优化的敏感性分析

研究了设计变量的随机特性,通过可靠度对随机变量的敏感性分析,导出系统可靠指标与设计随机变量参数之间的近似关系式,构造出近似的系统可靠度约束函数和相应的优化模型,给出其优化求解的过程,并给出算例以说明其实用性。     

航天器天线桁架结构多目标优化设计

针对有附加结构的卫星天线桁架结构,提出了一种实现结构多目标优化的综合设计方法。首先,探讨了附加结构刚度对桁架结构动力学特性的影响,以便建立精确的有限元模型,为进行优化设计奠定基础。之后,交替采用代理模型方法和人机交互方式进行结构拓扑构型设计。其中代理模型是采用优化拉丁超立方法进行试验设计,结合径向基函数近似方法生成的。最后,应用NSGA-II全局优化方法实现以重量最小化和频率最大化的多目标优化设计,并根据分层图定量可视化地从Pareto前端和Pareto最优解集中筛选最优设计方案。优化结果表明,相对于初始方案可以在基频几乎不变的情况下,重量减小29.66%。该方法有利于提高设计效率,降低全局优化的复杂度,同时能够得到满足设计要求的设计方案,适用于多目标结构优化设计。     

板壳结构满应力设计及在MSC/Nastran软件上的实现

根据满应力准则和板壳结构的应力与内力的关系,推导了求解板壳结构满应力设计的迭代关系式。采用无量纲设计变量实现变量连接,一个设计变量可以控制多个不同厚度的单元,扩大了程序的适用范围。在MSC/Nastran软件的基础上开发了适用于多工况、多变量的板壳满应力优化程序。利用Nastran的开放性,借助Pat-ran提供的PCL(Patran Command Language)开发环境,程序完全和Patran及Nastran融为一体。首先在Patran中建立有限元模型,利用Nastran进行有限元分析,按照满应力准则对设计变量调整,然后再次利用Nastran进行分析,这样反复迭代直到结构重量收敛。数值算例表明算法的可靠性、精确性和高效性,程序能够满足工程实际需要。     

应力和位移约束下的板壳结构截面优化

将准则法和数学规划法相结合，根据满应力准则将应力约束化为动态下限，借助单位虚载荷法将位移约束转化为设计变量的近似显函数，建立了满足应力和位移约束的优化模型. 为了解决多变量的大型优化问题，根据对偶理论将上千设计变量的优化模型转化为几个变量的对偶模型，并通过二次规划求解. 以MSC/Nastran软件为结构分析的求解器，借助MSC/Patran软件为开发平台，完成了板壳结构截面优化程序. 程序完全和Patran及Nastran融为一体，在Patran中建立模型，利用Nastran分析计算，根据优化结果对设计变量调整，再用Nastran进行结构重分析，反复迭代直到结构重量收敛. 算例表明程序的合理性和有效性，能够满足工程设计的需要.     

Evolutionary algorithm-based PID controller tuning for nonlinear quarter-car electrohydraulic vehicle suspensions

The basic challenge associated with the design of vehicle suspension system is the attainment of an optimal trade-off between the various design objectives. This study presents the design of proportional-integral-derivative (PID) controller for a quarter-car active vehicle suspension system (AVSS) using evolutionary algorithms (EA) such as the particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE). Each of the EA-based PID controllers showed overall improvement in suspension travel, ride comfort, settling time and road holding from the manually tuned controller and the passive vehicle suspension system. These improvements were, however, achieved at the cost of increased actuator force, power consumption and spool-valve displacement. DE-optimized PID control resulted in the best minimized suspension performance, followed by the GA and PSO, respectively. Frequency-domain analysis showed that all the signals were attenuated within the whole body vibration frequency range and the EA-optimized controllers had RMS frequency weighted body acceleration of the vehicle within allowable limits for vibration exposure. Robustness analysis of the DE-optimized PID-controlled AVSS to model uncertainties is carried out in the form of variation in vehicle sprung mass loading, tyre stiffness and speed.     

New analytical method to evaluate the powerplant and chassis coupling in the improvement vehicle NVH

The design of an automotive powerplant mounting system is an essential part in vehicle safety and improving the vehicle noise, vibration and harshness (NVH) characteristics. One of the main problems encountered in the automotive design is isolating low frequency vibrations of the powerplant from the rest of the vehicle. The significant powerplant mass makes the choice of frequency and mode arrangements a critical design decision. Several powerplant mounting schemes have been developed to improve NVH properties concentrating on the positioning and design of resilient supports. However these methods are based on decoupling rigid body modes from a grounded powerplant model which ignores chassis and suspension system interactions. But it cannot be stated that decoupling the grounded rigid body modes of the powerplant will systematically reduce chassis vibrations. In this paper, a new analytical method is proposed to examine the mechanisms of coupling between the powerplant and the vehicle chassis and subsystems. The analytical procedure expands the equation of motion of the vehicle components to such that a domain of boundary conditions used in the 6 degrees-of-freedom powerplant mounting model can be defined. An example of this new procedure is given for improving NVH chassis response at idle speed using the torque roll axis decoupling strategy.     

Optimum vehicle suspension designs by computer simulations

Computer simulation techniques are being used by vehicle suspension designers in an effort to obtain the optimum combination of suspension components to provide the maximum cross-country mobility for a vehicle. The ultimate effectiveness of the suspension will be dependent upon the ability of the computer simulation to accurately compute the dynamic responses of the vehicle as it traverses a cross-country terrain profile. The high degree of accuracy can only be obtained by exercising great care in the mathematical modelling procedures. Actual dynamic characteristics of the vehicle and suspension are required, which include their non-linear and discontinuous characteristics which develop as the vehicle traverses a cross-country terrain profile. When extreme care is exercised during the development of the mathematical model, the computer analysis of vehicle response will correlate within a few per cent of actual full-scale test values. This suspension technique will provide the suspension designer with a reliable method of obtaining an optimum design in a short period of time at a low programme cost.     

Design of a double wishbone front suspension for an orchard–vineyard tractor: Kinematic analysis

This paper deals with the design and implementation of a double wishbone front suspension for a vineyard–orchard tractor, developed in conjunction with a major tractor brand.To date, independent front suspensions are only found on commercial tractors over 150 kW. A front suspended axle is recognized as a popular option in improving tractor ride performance on larger vehicles. Despite their narrow track, vineyard–orchard tractors are required to have good lateral stability and stability on slopes (i.e. at least 28° rollover angle) and an extremely tight turning diameter for a 4WD vehicle (less than 7 m).The discussion is concered with retrofitting an existing vehicle with a double wishbone front suspension.This paper focuses on the layout and kinematic analysis phases of the design process. These were conducted in collaboration with the vehicle manufacturer to demonstrate suspension feasibility in terms of available space and correct kinematic layout.The final kinematic turning diameter obtained is about 6.4 m, with a ±65 mm suspension travel available. The roll centre height value is not very sensitive to steering (about −95 mm excursion in the Z axis from no-steer position to full steer).     

OPTIMAL DAMPING MATCHING Of SHOCK ABSORBER FOR A LIGHT TRUCK SUSPENSION SYSTEM

阻尼匹配是制约车辆悬架系统减振器设计的关键问题.以某轻型卡车为研究对象,利用MATLAB软件建立了悬架阻尼优化设计的半车模型.采用车体垂向加速度、俯仰角加速度和车轮动载均方根值作为评价指标,利用线性加权和法建立了悬架阻尼优化设计的目标函数.在随机路面激励下,对悬架系统阻尼进行了优化匹配和分析,并通过实车实验验证了优化效果.研究结果表明,悬架阻尼的匹配优化可有效提高车辆的行驶平顺性,从而为车辆悬架的动态设计提供有益参考.     

A spatial motion analysis model of tracked vehicles with torsion bar type suspension

A spatial motion analysis model for high-mobility tracked vehicles was constructed for evaluation of ride performance, steerability, and stability on rough terrain. Ordinary high-mobility tracked vehicles are equipped with independent torsion bar type suspension system, which consists of road arms and road wheels. The road arm rotates about the axis of torsion bar, and rigidity of the torsion bar and cohesion of damper absorb sudden force change exerted by interaction with the ground. The motion of the road arms should be considered for the evaluation of off-road vehicle performance in numerical analysis model. In order to obtain equations of motion for the tracked vehicles, the equations of motion for the vehicle body and for the assembly of a road wheel and a road arm were constructed separately at first. Two sets of equations were reduced with the constraint equations, which the road arms are mechanically connected to the vehicle body. The equations of motion for the vehicle have been expressed with minimal set of variables of the same number as the degrees of freedom for the vehicle motion. We also included the effect of track tension in the equations without constructing equations of motion for the tracks. Numerical simulation based on the vehicle model and experiment of a scale model passing over a trapezoidal speed bump were performed in order to examine the numerical model. It was found that the numerical results reasonably predict the vehicle motion.     

Stochastic optimal active control of a half-car nonlinear suspension under random road excitation

The random response analysis and the stochastic optimal active control of a half-car model with nonlinear suspension stiffness and damping traversing a rough road are studied in this paper. The road roughness height is modeled as the output of a first-order linear filter to Gaussian white noise. Considering the hysteretic nonlinear stiffness and the square damping of the vehicle model, the response statistics of the nonlinear suspension with active control are obtained by using the equivalent linearization method. The performance indexes of the active suspension are evaluated and compared with those of the corresponding passive suspension. It is found that the nonlinear active suspension gives a better vehicle performances like ride comfort, suspension stroke and overall performance. Finally, the theoretical results are verified through Monte Carlo simulation.     

Integration of uniform design and quantum-behaved particle swarm optimization to the robust design for a railway vehicle suspension system under different wheel conicities and wheel rolling radii

This paper proposes a systematic method, inte-grating the uniform design(UD)of experiments and quantum-behaved particle swarm optimization(QPSO),to solve the problem of a robust design for a railway vehicle suspension system. Based on the new nonlinear creep model derived from combining Hertz contact theory, Kalker's linear the-ory and a heuristic nonlinear creep model,the modeling and dynamic analysis of a 24 degree-of-freedom railway vehi-cle system were investigated.The Lyapunov indirect method was used to examine the effects of suspension parameters, wheel conicities and wheel rolling radii on critical hunting speeds.Generally,the critical hunting speeds of a vehicle sys-tem resulting from worn wheels with different wheel rolling radii are lower than those of a vehicle system having origi-nal wheels without different wheel rolling radii.Because of worn wheels, the critical hunting speed of a running rail-way vehicle substantially declines over the long term. For safety reasons,it is necessary to design the suspension sys-tem parameters to increase the robustness of the system and decrease the sensitive of wheel noises.By applying UD and QPSO,the nominal-the-best signal-to-noise ratio of the sys-tem was increased from?48.17 to?34.05 dB.The rate of improvement was 29.31%.This study has demonstrated that the integration of UD and QPSO can successfully reveal the optimal solution of suspension parameters for solving the robust design problem of a railway vehicle suspension sys-tem.     

伴随变阻尼作用的干摩擦下的车辆系统非线性动力学分析

对分段线性阻尼和干摩擦共同作用下的车辆悬挂系统进行了非线性动力学分析研究，阐述了判定系统周期运动稳定性的理论方法；利用数值模拟方法分析了具有不同阻尼参数组合的系统对简谐激励的振动响应，并分析了由干摩擦引起的粘-滑振动行为．结果表明：提高摩擦力对抑制响应有利，但车辆系统在低速下运行时会出现复杂的粘-滑振动，轮轨之间产生较大的瞬时刚性冲击；而通过增加轮对与侧架的弹性悬挂可以有效减弱这种瞬时刚性冲击．     

An augmented multicrack elastoplastic damage model for tensile cracking

In this paper we present the general formulation and numerical aspects of an augmented multicrack elastoplastic damage model aiming to reflect the crack induced anisotropy in concrete like quasi-brittle materials. Consistent evolution laws for the involved internal variables are derived based on the augmented Lagrangian method. The (time) discrete formulation and the corresponding variational structure are investigated, with the Euler–Lagrangian equations defining the closest-point projection approximation of the proposed model. The numerical aspects, such as the stress updating algorithm and the algorithmic consistent tangent moduli, are also discussed in details. It is found that in the developed numerical algorithm the active loading surfaces are determined in such a posterior manner that potential numerical problems due to the iteratively updating procedure in classical algorithms can be avoided. The proposed model is applied to the modeling of tensile cracking in concrete. The behavior of a single crack is characterized by an elliptical cracking surface and a hyperbolic softening function, with the orientations of potential cracks determined by Mohr’s postulate. The model is verified by calculating the single point stress vs. strain relations of concrete under several typical proportional and non-proportional loading cases. Finally, two benchmark tests of concrete structures, i.e. four-point bending beam under cyclic loading (Hordijk, 1992) and double edge notched specimens under mixed tension/shear forces (Nooru-Mohamed, 1992), are numerically simulated. Both predicted load vs. displacement curves and crack patterns agree well with the experimental data.