Probabilistic crack trajectory analysis by a dimension reduction method

This paper proposes a novel analysis method of stochastic crack trajectory based on a dimension reduction approach. The developed method allows efficiently estimating the statistical moments, probability density function and cumulative distribution function of the crack trajectory for cracked elastic structures considering the randomness of the loads, material properties and crack geometries. First, the traditional dimension reduction method is extended to calculate the first four moments of the crack trajectory, in which the responses are eigenvectors rather than scalars. Then the probability density function and cumulative distribution function of the crack trajectory can be obtained using the maximum entropy principle constrained by the calculated moments. Finally, the simulation of the crack propagation paths is realized by using the scaled boundary finite element method. The proposed method is well validated by four numerical examples performed on varied cracked structures. It is demonstrated that this method outperforms the Monte Carlo simulation in terms of computational efficiency, and in the meanwhile, it has an acceptable computational accuracy.     

Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment

This paper proposes a scenario-based two-stage stochastic programming model with recourse for master production scheduling under demand uncertainty. We integrate the model into a hierarchical production planning and control system that is common in industrial practice. To reduce the problem of the disaggregation of the master production schedule, we use a relatively low aggregation level (compared to other work on stochastic programming for production planning). Consequently, we must consider many more scenarios to model demand uncertainty. Additionally, we modify standard modelling approaches for stochastic programming because they lead to the occurrence of many infeasible problems due to rolling planning horizons and interdependencies between master production scheduling and successive planning levels. To evaluate the performance of the proposed models, we generate a customer order arrival process, execute production planning in a rolling horizon environment and simulate the realisation of the planning results. In our experiments, the tardiness of customer orders can be nearly eliminated by the use of the proposed stochastic programming model at the cost of increasing inventory levels and using additional capacity.     

Lateral inventory transshipment problem in online-to-offline supply chain

Online-to-offline (OTO) is a new commercial model with enormous market potential. Online customer orders are forwarded to the offline brick-and-mortar store to fulfil, which is a combination of dual-channel supply chain. OTO overcomes many disadvantages of the traditional dual-channel supply chain, but still faces uncertain market demand. To reduce the inventory risk caused by demand uncertainty, lateral inventory transshipment is employed in this paper to pool inventory risk in OTO supply chain. We model centralised OTO and decentralised OTO with/without transshipment, and then analyse different scenarios. Our results demonstrate that there exists a unique Nash equilibrium of inventory order levels in dual channels and an optimal transshipment price to maximise the profit of the entire supply chain. Finally, we provide a numerical example of uniform demand distribution. Our analyses offer many managerial insights and show that transshipment always benefits the OTO supply chain.     

A mathematical model for vehicle routing problem under endogenous uncertainty

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.     

Achieving robust design through statistical effect screening

This work proposes a method for statistical effect screening to identify design parameters of a numerical simulation that are influential to performance while simultaneously being robust to epistemic uncertainty introduced by calibration variables. Design parameters are controlled by the analyst, but the optimal design is often uncertain, while calibration variables are introduced by modeling choices. We argue that uncertainty introduced by design parameters and calibration variables should be treated differently, despite potential interactions between the two sets. Herein, a robustness criterion is embedded in our effect screening to guarantee the influence of design parameters, irrespective of values used for calibration variables. The Morris screening method is utilized to explore the design space, while robustness to uncertainty is quantified in the context of info‐gap decision theory. The proposed method is applied to the National Aeronautics and Space Administration Multidisciplinary Uncertainty Quantification Challenge Problem, which is a black‐box code for aeronautic flight guidance that requires 35 input parameters. The application demonstrates that a large number of variables can be handled without formulating simplifying assumptions about the potential coupling between calibration variables and design parameters. Because of the computational efficiency of the Morris screening method, we conclude that the analysis can be applied to even larger‐dimensional problems. (Approved for unlimited, public release on October 9, 2013, LA‐UR‐13‐27839, Unclassified.) Copyright © 2015 John Wiley & Sons, Ltd.     

An efficient hybrid reliability analysis method with random and interval variables

Random and interval variables often coexist. Interval variables make reliability analysis much more computationally intensive. This work develops a new hybrid reliability analysis method so that the probability analysis (PA) loop and interval analysis (IA) loop are decomposed into two separate loops. An efficient PA algorithm is employed, and a new efficient IA method is developed. The new IA method consists of two stages. The first stage is for monotonic limit-state functions. If the limit-state function is not monotonic, the second stage is triggered. In the second stage, the limit-state function is sequentially approximated with a second order form, and the gradient projection method is applied to solve the extreme responses of the limit-state function with respect to the interval variables. The efficiency and accuracy of the proposed method are demonstrated by three examples.     

活塞式液体流量标准装置体积校准方法的探讨

对活塞式液体流量标准装置体积校准方法进行了研究,基于理想圆柱体模型建立了活塞装置体积模型,引入修正系数对所建立的体积模型进行修正,并利用质量守恒定律提出采用质量法对活塞装置进行体积校准.对修正系数进行赋值分析和不确定度评定,结果表明5L及以上体积的扩展不确定度优于0.05％.该方法操作简便,可控性好,结果准确可靠.     

化学危险品事故源强不确定性实例分析

讨论了化学危险品突发事故的环境危害评价的不确定性问题。应用几率密度函数可解决事故预测时源强估算的不确定性问题。采用模糊集方法可解决应急管理时事故源强的不确定性问题。文章提供了液氯泄漏和丙烷闪蒸─—火球模型两个实例。     

新型军械装备损坏程度评估方法研究

根据新型军械装备损坏程度具有不确定性的特点,提出了基于D-S证据理论的新型军械装备损坏程度评估方法,并求出了新型军械装备损坏程度区分.通过对典型新型军械装备损坏程度的评估,验证了该方法的有效性和实用性.