偏最小二乘回归在响应面法可靠度分析中的应用

针对目前多维变量可靠度问题中广泛应用的均匀设计响应面法,分析了采用最小二乘法拟合样本数据回归模型时存在的局限性,并在已有方法的基础上提出了一种改进的方法。该方法将均匀设计与偏最小二乘回归技术相结合来回归响应面模型,从而计算结构的失效概率,有效的解决了变量间多重相关性及小样本条件下建立回归模型的问题。通过算例验证了该方法的适用性,尤其对于高维变量的可靠度问题,与最小二乘拟合响应面相比,计算结果更加精确。     

基于切平面布点的一种改进响应面方法

基于合理选择试验点的位置,该文提出一种改进响应面方法。该方法首先在经过设计点的切平面上布置试验点,然后沿切平面法向量方向移动试验点,并利用设计点和先前试验点的信息布置加强试验点。所布置的试验点既对设计点附近区域给予足够重视,同时又考虑极限状态函数在设计点附近区域的变化趋势,进而提高响应面函数在设计点附近区域的拟合精度。在响应面函数的拟合过程中,该文方法能够保证响应面函数在设计点处是无误差的,进一步提高失效概率的评估精度。算例表明,对于显式和隐式极限状态函数,该方法均具有较好的效率和精度。     

基于改进均匀设计响应面的桥梁地震易损性分析

为研究传统均匀设计响应面法中设计变量多重相关性现象和变量相关性条件对地震易损性分析的影响,引入Nataf变换,结合基于样条变换的均匀设计响应面法,提出了一种基于改进均匀设计响应面的桥梁地震易损性分析方法。以一座多跨连续梁桥为例,基于Open Sees建立其动力有限元模型并进行非线性时程分析,考虑了墩柱、板式橡胶支座、铅芯橡胶支座和桥台四类构件的地震损伤,分别在考虑变量相关性前后、采用传统及改进均匀设计响应面法对算例桥梁地震易损性分析进行了比较。研究结果表明,考虑变量相关性后,改进均匀设计响应面法建立的响应面模型能更好地拟合结构功能极限状态函数;桥梁构件及系统在不同损伤状态下的损伤超越概率均有一定程度的降低;忽略变量相关性的影响、采用传统均匀设计响应面法均可能会高估桥梁结构在地震作用下的易损程度。     

基于Kriging改进响应面法的桥梁地震动力可靠度研究

鉴于桥梁结构对地震响应的非线性和复杂性等问题,提出了基于Kriging改进响应面法的桥梁结构地震动力可靠度分析方法。首先利用Kriging模型的优越模拟性能,将其作为响应面函数,并采取自适应策略加以改进,而后采取线性过滤器脉冲响应法对地震随机激励荷载进行了离散,并基于首次超越问题的定义建立了动力可靠度极限状态方程,最后对桥梁结构的地震可靠度问题进行了分析。计算分析结果表明:提出的基于Kriging模型的改进响应面法能有效完成桥梁地震动力可靠度的计算分析(包括结构参数随机性对桥梁动力可靠度的影响),且结果具有较高的准确性和高效性。     

基于自适应响应面法的输电塔线体系腐蚀疲劳可靠度研究

环境腐蚀和风振疲劳耦合作用下输电塔体的结构性能逐渐退化,满足预定设计功能的概率减小。然而,传统响应面法计算结构可靠度时均不能兼顾"效率"和"精度"。为此,首先通过严格的数学推导给出了交叉项是否存在的判断准则,将该判断准则与传统二次响应面法相结合建立了考虑部分交叉项的自适应响应面法。然后,通过Q345等边角钢腐蚀疲劳试验结果给出了构件腐蚀疲劳t-P-S-N曲线方程,再与概率论相结合建立了随机疲劳曲线方程。最后,通过工程算例采用建议自适应响应面法以风速、腐蚀时间和随机腐蚀疲劳S-N曲线方程为随机变量对输电塔线体系进行了腐蚀疲劳可靠度研究,结果表明:①交叉项判断准则能有效地保留相互影响随机变量之间的交叉项;②建议自适应响应面法在满足精度的同时能有效减少计算量;③构件随机腐蚀疲劳S-N曲线模型在结构可靠性分析中简单易行。     

基于神经网络响应面法的随机结构动力可靠度分析

在对神经网络响应面法的原理和算法进行研究的基础上，建立了基于神经网络响应面法的随机结构动力可靠度分析方法。首先，基于首次超越破坏准则，参照静力可靠度的功能函数模式，建立了随机结构的动力可靠度功能函数；然后引入响应面法，以三层BP神经网络作为拟合函数，推导了功能函数的拟合表达式；最后结合一次二阶矩方法求解可靠指标。算例分析表明了本文方法有较好的计算精度和计算效率，在复杂结构的动力可靠度分析中有较强的实用价值。     

基于随机响应面法的结构可靠度分析

提出了考虑变量间相关性的随机响应面法,采用正交变换解决随机响应面法输入随机变量间相关性问题。推导了4阶和5阶Hermite随机多项式展开的解析表达式。编写了基于C#语言的随机响应面法计算程序。最后采用算例证明了随机响应面法在结构可靠度分析中的有效性。结果表明,提出的随机响应面法能够有效地分析输入随机变量间相关性的可靠度问题。3阶随机响应面法的计算精度在大多数情况下可以满足结构可靠度分析的需要,而且计算效率较高。但是随着变量间相关性的增加,4阶或5阶随机响应面法才能保证足够的计算精度。概率配点数目为随机多项式待定系数数目的两倍并不总能保证足够的计算精度,一般来说,配点数目要大于两倍待定系数的个数才能保证随机响应面法足够的计算精度。     

MTMD控制下随机结构的动力可靠度分析

考虑到实际工程结构的不确定性,基于遗传优化的神经网络响应面法,进行了MTMD控制下随机结构的动力可靠度分析,并对TMD及MTMD控制下结构的动力可靠度进行对比。该方法不仅具有传统神经网络响应面法的特性,而且引进了遗传算法的全局随机搜索的优点,可以精确地逼近随机结构的功能函数表达式,有效地减少用JC法求解可靠度指标的迭代次数,节省时间。算例分析表明了本文方法的有效性和准确性,对于随机结构,MTMD比TMD能更好地提高结构的动力可靠度。     

多自由度结构动力可靠度分析的小波方法

该文发展了基于小波分析的局部平稳法在多自由度结构动力可靠度中的应用。首先,基于广义谐和小波和随机过程的局部平稳小波模型,发展了线性多自由度结构系统在各时间-频率子域上激励功率谱与响应功率谱之间的关系,并计算得到了在一般随机动力激励下结构随机动力响应功率谱密度和各阶谱矩。随后,根据随机动力激励和响应的高斯假定及超越过程的Markov假定,得到了线性多自由度结构在均匀/非均匀调制随机激励下层间位移的动力可靠度指标。结构动力可靠度的Monte Carlo模拟显示了所提方法的可靠性与计算高效性。     

基于响应面法和Morgenstern-Price法土坡可靠度计算方法

基于响应面法,建立了一种高效的边坡可靠度指标和失效概率近似计算方法。该法在构造响应面函数时,抽样点计算采用Morgenstern-Price法取代传统费时的有限单元法,大大降低了计算工作量。利用Monte-Carlo随机抽样原理,提出了一种能同时确定边坡最危险非圆弧滑动面和最小可靠度指标的随机搜索新算法。该文给出的两个算例验证了方法的实用性和可靠性,其计算结果同时表明:当分别以最小可靠度指标和最小中值安全系数为目标函数时,搜索到的边坡最危险滑动面相差较大。最后,探讨了土性指标(c,φ)的分布概型及相关性对边坡可靠度计算结果的影响。     

Optimal design of heating channels for rapid heating cycle injection mold based on response surface and genetic algorithm

Rapid heating cycle molding (RHCM) technology is a novel polymer injection molding method developed in recent years. In this paper, the principle of RHCM was introduced and a RHCM mold for producing a large-size LCD TV panel was presented. Aiming at achieving a uniform temperature distribution on the cavity surface of the stationary mold insert, the distances between the neighbor heating channels were considered as the main design variables. An objective function for optimizing the temperature distribution uniformity was proposed. The experiment samples for calculating the objective function were selected by using the Latin Hypercube Design experiment method. A quadric response surface equation for calculating temperature distribution uniformity was established. The design variables were optimized by using genetic algorithm and the optimal solutions were obtained. The temperature distribution uniformity on the stationary mold insert cavity surface was greatly improved. The effectiveness of the optimization method presented in this paper was also demonstrated by industrial injection production of a LCD TV panel.     

Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis

The non-probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non-probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space-filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non-probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.     

A new artificial neural network-based response surface method for structural reliability analysis

This paper presents a new artificial neural network-(ANN)based response surface method in conjunction with the uniform design method for predicting failure probability of structures. The method involves the selection of training datasets for establishing an ANN model by the uniform design method, approximation of the limit state function by the trained ANN model and estimation of the failure probability using first-order reliability method (FORM). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the limit state function and then provides a less rigorous formulation in the context of FORM. Results of three numerical examples involving both structural and non-structural problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Compared with the conventional ANN-based response surface method, the proposed method is much more economical to achieve reasonable accuracy when dealing with problems where closed-form failure functions are not available or the estimated failure probability is extremely small. Finally, several important parameters in the proposed method are discussed.     

Technologic parameter optimization of gas quenching process using response surface method

A step function model with time is presented in the paper, and an axisymmetric component is regarded as the study objective in this model. The heat transfer coefficient during the gas quenching process is described as a function of time in this model, and five design variables are selected to do the design of Box–Behnken experiment with five factors and three levels. The levels of design variables that attain from the result of Box–Behnken experiment design are regard as the technical parameters of gas quenching to simulate the gas quenching process using the FEM software developed in the paper. Some mathematical models of response surface are gained by the mixed regression method and response surface method. These mathematical models show the dependencies of distortion, surface average equivalent residual stress, standard deviation of equivalent residual stress, average surface hardness and standard deviation of surface hardness with respect to the design variables. The optimization model is presented with the distortion as the optimization objective, and the model is optimized with an upper limit, a lower limit and the constraint function by the non-linear method and the Lagrange multiplier method.     

基于近似模型的空调配管阻尼层优化设计

空调配管系统的减振降噪是空调结构开发中的一个设计难点,是制约空调整体品质的一个关键参数。针对空调仿真优化设计中计算成本和计算精度之间的矛盾,本文将统计学中的近似模型技术应用到空调配管系统的阻尼优化。采用正交试验设计与均匀试验设计相结合的试验设计方法,建立了多项式响应面、Kriging最优内插、BP神经网络近似模型,研究了阻尼层位置、宽度等参数与结构响应频率、阻尼比之间的近似映射关系。最后采用多目标遗传算法分析了结构阻尼比与结构质量之间的Pareto曲线,并选择最优结果进行了试验验证。研究表明,采用近似模型的阻尼层优化方法可以有效地提高设计效率,降低成本,为空调系统的仿真提供了一种可行的方法。     

基于类等势场和响应面法的复杂锻件预成形优化设计

为实现复杂锻件的预成形设计,以连杆的热锻预成形设计为研究对象,建立基于类等势场和响应面分析的三维复杂锻件的预成形设计方法。在分析毛坯与终锻件间等势场分布规律与特点的基础上,采用逆向拟合法提取等势面及线面光顺处理,实现等势面的高效精确重构。针对长轴类锻件的预成形设计要求,提出沿零件的长、宽、高分别设置合理的缩放因子的非均匀缩放方法。实现了预成形件材料分布的合理调控,获得了优化的预锻件和辊锻毛坯,最终获得了充填完整、无任何成形缺陷且飞边小的连杆终锻件。数值模拟结果表明,所建立的方法能较好实现复杂锻件的预成形优化设计。     

Application of a Ge semi-conductor detector to whole-body counter

To calibrate a whole-body counter, it is necessary to find a determination method for peak efficiencies of detectors used in the whole-body counter. For this purpose, peak efficiencies of a Ge semiconductor detector for point and volume sources were evaluated in the photon energy range 60-1836 keV by Monte Carlo simulation and experiment. It was found that the calculated peak efficiency curves as a function of energy without modelling of the actual sensitive region of the detector are similar in shape to those measured. The calculated peak efficiencies of the detector having an apparent dead layer (1 mm) were also found to agree with the experimental values (deviations from -10-24%). Consequently, the simulation method for peak efficiencies was validated. In addition, an optimum design for a whole-body counter with Ge semiconductor detectors was examined by simulation. This simulation provides a method to determine an optimum arrangement of detectors in a whole-body counter, offering a uniform response to various 137Cs distributions in a human body.     

Direct numerical simulation of ignition of a single particle freely moving in a uniform flow

In this study, a direct numerical simulation (DNS) of the ignition of a single particle freely moving in a uniform flow is performed to investigate the particle’s ignition behavior in detail. The Arbitrary Lagrangian-Eulerian (ALE) method is employed to compute the six degrees of freedom motion of a particle (Zhang et al., 2015). The computational setting follows the experiment designed by Lee and Choi (2015). The volatile gas that is composed of methane blows out at the particle surface. Its velocity is calculated by Ex-CPD model (Umemoto et al., 2017) and its direction is set perpendicular to the particle surface. The ignition behavior is compared with that observed in the experiment. The effect of the particle’s shape is also investigated. Results show that the ignition delay of the particle and the flame inclined angle are in good agreement with that of the experiment. While examining the combustion of the gas phase by considering the variation of Flame Index (FI), it is found that a premixed and diffusion regions are formed around the particle after the devolatilization starts. The gas phase ignites at the boundary of the premixed and diffusion regions and the flame propagates towards the particle. This causes a rapid increasing of the temperature and the volatile velocity on the particle surface. Finally, a diffusion flame is formed and reaches a stable state around the particle. It is also revealed that the flame keeps spherical despite the spheroidal shape of the particle.     

Stochastic analysis and robust optimization for a deck lid inner panel stamping

FE-simulation and optimization are widely used in the stamping process to improve design quality and shorten development cycle. However, the current simulation and optimization may lead to non-robust results due to not considering the variation of material and process parameters. In this study, a novel stochastic analysis and robust optimization approach is proposed to improve the stamping robustness, where the uncertainties are involved to reflect manufacturing reality. A meta-model based stochastic analysis method is developed, where FE-simulation, uniform design and response surface methodology (RSM) are used to construct meta-model, based on which Monte-Carlo simulation is performed to predict the influence of input parameters variation on the final product quality. By applying the stochastic analysis, uniform design and RSM, the mean and the standard deviation (SD) of product quality are calculated as functions of the controllable process parameters. The robust optimization model composed of mean and SD is constructed and solved, the result of which is compared with the deterministic one to show its advantages. It is demonstrated that the product quality variations are reduced significantly, and quality targets (reject rate) are achieved under the robust optimal solution. The developed approach offers rapid and reliable results for engineers to deal with potential stamping problems during the early phase of product and tooling design, saving more time and resources.     

基于响应面法的刀口金属密封结构优化设计

以有限元数值模拟为手段,通过一阶响应面建模,确定了满足密封判据的刀口金属密封结构设计参数的范围。采用均匀设计,建立了以设计参数为变量,以有效密封面宽、最大接触应力为响应的二阶响应面模型,并利用多目标优化方法和遗传算法,对响应面模型进行了优化求解,得到了优化的设计参数组合。有限元验证结果显示,优化后的密封结构具有更好的密封性能。