捷联惯导大失准角误差模型在快速传递对准中的应用

针对快速传递对准中主子惯导相对姿态存在大角度的情况,推导了捷联惯导大失准角误差模型.该模型采用欧拉角表示姿态误差,并用欧拉运动方程准确描述其传播规律.鉴于该模型中的姿态观测方程是复杂的非线性函数,采用无需求导的UKF算法,并采用奇异值分解(SVD)解决方差阵的病态问题.仿真结果表明,该算法在小角度误差条件下滤波精度优于线性模型,并且适用于大角度误差条件.     

四元数长方矩阵的同时复对角化

利用四元数矩阵的奇异值分解(SVD),对两个四元数长矩阵给出了其同时复对角化的充要条件,进一步对一个四元数长矩阵集合,针对其同时复对角化问题,给出了一系列充分必要条件.     

一种利用GPS载波相位姿态测量的方法

GPS初始整周模糊度的求解是利用载波相位进行测量时的关键问题.采用了对系数矩阵进行QR分解的方法,用以降低矩阵的维数.模糊度搜索时,针对Z变换可能会引入多余误差,采用了对称三角分解法对协方差矩阵进行去相关处理.实验与仿真结果表明,定位误差在0.5 cm以内,方位角和仰角误差在0.1°以内.     

Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model

In this article, we consider a multi‐product closed‐loop supply chain network design problem where we locate collection centers and remanufacturing facilities while coordinating the forward and reverse flows in the network so as to minimize the processing, transportation, and fixed location costs. The problem of interest is motivated by the practice of an original equipment manufacturer in the automotive industry that provides service parts for vehicle maintenance and repair. We provide an effective problem formulation that is amenable to efficient Benders reformulation and an exact solution approach. More specifically, we develop an efficient dual solution approach to generate strong Benders cuts, and, in addition to the classical single Benders cut approach, we propose three different approaches for adding multiple Benders cuts. These cuts are obtained via dual problem disaggregation based either on the forward and reverse flows, or the products, or both. We present computational results which illustrate the superior performance of the proposed solution methodology with multiple Benders cuts in comparison to the branch‐and‐cut approach as well as the traditional Benders decomposition approach with a single cut. In particular, we observe that the use of multiple Benders cuts generates stronger lower bounds and promotes faster convergence to optimality. We also observe that if the model parameters are such that the different costs are not balanced, but, rather, are biased towards one of the major cost categories (processing, transportation or fixed location costs), the time required to obtain the optimal solution decreases considerably when using the proposed solution methodology as well as the branch‐and‐cut approach. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

SPH并行计算方案及其在自由表面流动模拟中的应用

针对光滑粒子动力学主要计算量是近邻粒子搜索这一特点,提出了一种基于粒子分解的光滑粒子动力学并行计算方案。利用该方案可以方便地将任意串行光滑粒子动力学代码并行计算,而且每一个时间步内的信息传递量只和粒子总数有关,而和粒子的分布无关,因而特别适合于自由表面流动等大变形问题的并行数值模拟。对一个粒子总数为40万的三维溃坝问题的模拟结果表明:此方案能达到的最大加速比约为16,这一结果可能比空间分解方案(不考虑动态负载均衡)更优。     

混合气体识别的响应等效性与瞬态信号正交分解模型

针对目前混合气体识别大多采用传感器稳态响应信号、基于线性混合假设或大量样本学习,而瞬态响应信号特征分析主要应用非正交分解的问题,提出一种基于响应等效性与瞬态信号正交分解的混合气体识别模型。分析金属氧化物半导体传感器对混合气体的响应特性,建立基于气体响应成分等效性假设的气体非线性混合模型,在此基础上,提出并应用一种新的正交基函数——扩展类Legendre正交基,对气体传感器瞬态响应信号进行分解;通过对正交分解系数与气体浓度的回归分析,验证二者之间的指数型关联关系,并以正交分解系数为特征参数,利用气体非线性等效混合模型对混合气体分解与辨识。实验结果表明,尽管这种混合气体识别模型仅用单一气体检测的先验知识,对混合气体的识别误差仍可达到15%以内。     

EEMD+BiGRU组合模型在短时交通流量预测中的应用

针对城市交通流随机波动性强、数据中含噪声多导致预测精度下降的问题,提出一种基于集合经验模态分解(ensemble empirical mode decomposition,EEMD)和双向门控循环单元(bidirectional gated recurrent unit,BiGRU)的组合交通流量预测模型,有效地提升了短时交通流预测的精度。模型利用EEMD算法对原始数据进行分解,根据分解所得的本征模函数(intrinsic mode function,IMF)分量绘制噪声能量图谱,去除分量中的噪声,并将去噪后的IMF分量作为BiGRU网络的输入进行训练,再将训练所得的结果进行重构加和,得到最终的预测结果。实验结果表明,未舍弃含有噪声的IMF分量进行重构的预测结果,相比于参考文献中提出的EMD+LSTM模型、LSTM模型和EEMD+LSTM模型,其平均绝对百分误差分别优化了42.36%、61.82%和30.95%;舍弃含有噪声的IMF分量后进行重构的预测结果,其平均绝对百分误差相比于将全部IMF分量进行重构优化了56.62%。     

On the hierarchy of γ‐valid cuts in global optimization

Concavity Cuts play an important role in concave minimization. In Porembski, J Global Optim 15 ( 17 ), 371–404 we extended the concept underlying concavity cuts which led to the development of decomposition cuts. In numerical experiments with pure cutting plane algorithms for concave minimization, decomposition cuts have been shown to be superior to concavity cuts. However, three points remained open. First, how to derive decomposition cuts in the degenerate case. Second, how to ensure dominance of decomposition cuts over concavity cuts. Third, how to ensure the finite convergence of a pure cutting plane algorithm solely by decomposition cuts. These points will be addressed in this paper. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

The probability of the existence of a feasible flow in a stochastic transportation network

Stochastic transportation networks arise in various real world applications, for which the probability of the existence of a feasible flow is regarded as an important performance measure. Although the necessary and sufficient condition for the existence of a feasible flow represented by an exponential number of inequalities is a well‐known result in the literature, the computation of the probability of all such inequalities being satisfied jointly is a daunting challenge. The state‐of‐the‐art approach of Prékopa and Boros, Operat Res 39 (1991) 119–129 approximates this probability by giving its lower and upper bounds using a two‐part procedure. The first part eliminates all redundant inequalities and the second gives the lower and upper bounds of the probability by solving two well‐defined linear programs with the inputs obtained from the first part. Unfortunately, the first part may still leave many non‐redundant inequalities. In this case, it would be very time consuming to compute the inputs for the second part even for small‐sized networks. In this paper, we first present a model that can be used to eliminate all redundant inequalities and give the corresponding computational results for the same numerical examples used in Prékopa and Boros, Operat Res 39 (1991) 119–129. We also show how to improve the lower and upper bounds of the probability using the multitree and hypermultitree, respectively. Furthermore, we propose an exact solution approach based on the state space decomposition to compute the probability. We derive a feasible state from a state space and then decompose the space into several disjoint subspaces iteratively. The probability is equal to the sum of the probabilities in these subspaces. We use the 8‐node and 15‐node network examples in Prékopa and Boros, Operat Res 39 (1991) 119–129 and the Sioux‐Falls network with 24 nodes to show that the space decomposition algorithm can obtain the exact probability of these classical examples efficiently. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 479–491, 2016     

希尔伯特-黄变换在脉冲涡流信号消噪与识别中的应用

针对传统方法无法有效识别不同尺寸细小裂纹所产生的脉冲涡流信号,提出一种基于希尔伯特-黄变换的脉冲涡流信号消噪与识别算法。对脉冲涡流信号进行集成经验模态分解并通过归一化自相关函数及其方差特性分选出含有噪声的本征模态函数;对含噪声的本征模态函数进行阈值消噪并与未做处理的本征模态函数重构成无噪声信号;对无噪声信号进行希尔伯特-黄变换并计算出希尔伯特边际谱;根据希尔伯特边际谱的差异识别出不同细小尺寸的表面与下表面裂纹。实验结果表明了所提方法的有效性,经过集成经验模态分解消噪,消除了噪声对脉冲涡流信号的干扰;而基于希尔伯特-黄变换的方法则能够有效识别出不同尺寸的裂纹。