Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models

Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.     

Optimal redesign decisions through failure rate estimates

To reduce the time-to-market of newly developed systems, manufacturers increasingly adopt strategies where systems are brought to market while system field reliability is still uncertain. These systems are typically sold under performance-based contracts, which incentivizes potential customers to invest in them despite reliability uncertainty. Such contracts make the manufacturer (partly) responsible for the availability of the system. Subsequently, when field reliability is lower than anticipated, the manufacturer may choose to redesign the system to avoid high contract penalties. Redesign is a costly effort which may substantially increase field reliability. Deciding when to redesign is challenging, especially because the initial failure rate estimate by the system's engineers is refined over time as failure data accrues. We propose a model that endogenizes the failure rate updating to analyze this tactical redesign decision. We study additive and multiplicative redesigns and show that the optimal policy has a control limit structure. We benchmark our optimal policy against a static counterpart numerically, and conclude that basing redesign decisions on the updated estimate of the failure rate can substantially reduce costs.     

失效概率函数求解的高效算法

结合基于分数矩约束的极大熵方法和替代模型法,发展了一种失效概率函数求解的高效算法。所提算法的基本思路是利用自主学习的迭代Kriging方法来构造失效概率函数,即采用较少的训练样本来构造粗糙的失效概率函数,在此基础上通过添加新的违反学习函数约束的样本来更新失效概率函数,直到达到精度要求。对于每一个分布参数的训练样本点,所提方法采用分数矩约束的极大熵法来求解相应的失效概率样本。由于分数矩的计算采用了高效的降维积分,并且由于分数矩约束下极大熵法中优化策略高效地逼近了响应的概率密度函数,从而使得失效概率样本能够被高效高精度地估计出来。为了检验所提方法的精度及效率,给出了两个算例,对比了所提方法与已有的失效概率函数求解的Bayes公式法及Monte Carlo法等,结果表明,所提方法适用于求解复杂的功能函数问题,且在满足精度要求的基础上大大降低了计算量。     

稳态法测量热系数的计算方法改进研究

不良导体热系数测量普遍采用的是稳态法,但表面散热率的间接测量和样品侧面散热与漏热给测量带来一定误差,使得热系数实际测量值略微偏大。介绍了新的实验装置和实验数值计算方法,并且分析研究了样品边缘（侧面）热损失的物理模型,提出了新的数学模型和数据处理方法,纠正了这些偏差,与实验吻合较好。     

粘性对高超声速飞行器攻角特性影响研究

采用二维耦合隐式NS方程和标准κ-ε湍流模型对高超声速飞行器在进气道关闭、发动机通流以及发动机点火工作状态下的内外流场进行了数值仿真研究,离散采用二阶迎风格式,分析了在不同攻角(-10°～7°)条件下,粘性对处于三种不同的工作状态下高超声速飞行器升力特性、阻力特性以及俯仰力矩特性的影响.结果表明,粘性对处于发动机通流和发动机点火工作状态下的飞行器气动-推进性能影响显著,尤其是阻力特性,粘性阻力占总阻力的比重超过50%.     

杂合数据的粗糙集属性约简方法

针对决策表中属性取值为杂合数据的情况,提出了基于粗糙集理论的属性约简算法.首先给出了对象间在杂合数据下的相似度计算定义.为了获取合理的对象集合的软划分,给出了阈值计算的最优化模型,并基于粗糙集的上、下近似的概念,得到对象集合在条件属性下的上、下近似的覆盖划分.之后,通过各对象基于条件属性和决策属性的上、下近似下的分布矩阵描述,利用最大分布矩阵,直观地得到两种不同观点下的约简结果.实验结果表明了本算法的合理和有效性.     

Traffic channeling under uncertain conversion rates on e-commerce platforms

Traffic is the lifeblood of every e-commerce platform. The question of how to channel traffic to merchants operating on a platform lies at the heart of platform management. We consider a platform on which two independent merchants sell their products. Merchants compete on inventory in the sense that some of the unmet demand at one merchant will spill over to the other. The platform channels traffic based on products' conversion rates to maximize the total sale on the platform. We show that traffic channeling plays three roles. First, it allows more efficient allocation of traffic; that is, the merchant with a high conversion rate is given a higher priority in receiving traffic. Second, it allows the platform to control demand spillover between the merchants to maximize total sales. The platform either facilitates or prevents demand spillover, depending on product substitutability. Third, traffic channeling intensifies competition between the merchants and hence increases the total inventory. More efficient allocation of traffic and the increase in inventory increase sales inequality between the merchants. In contrast, demand spillover decreases sales inequality. While the platform always benefits from traffic channeling, the merchants do not benefit when their products are moderately substitutable. Interestingly, when the two products are owned and sold by the same merchant, the opposite happens–traffic channeling always benefits the merchant but may hurt the platform. Our study provides a basis for informed discussions on how platforms should channel traffic in response to conversion rates, and how traffic channeling affects the welfare of merchants and platforms.