稀土分离联产品质量控制研究

以稀土分离企业为背景,抽取联产品特点及质量属性,绘制单一产品的指数加权移动平均控制图和联产品的多元残差T²控制图,并将两类控制图进行对比分析,分析表明和EWMA控制图相比,联产品多元残差T²控制图能降低控制图虚发警报的概率。针对多元残差T²控制图发现的异常模式,采用支持向量机模型对异常模式进行分类处理,寻找分类规则,构造PSO-SVM分类器,运用粒子群算法对SVM参数寻优,并对得出的结果进行对比分析。分析表明该分类器能提高分类正确率,模式识别可以用于诊断稀土企业引起联产品多元残差T²控制图出现异常的原因,从而提高过程质量管理水平。     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

点光源哈特曼最优阈值估计方法研究

针对夏克-哈特曼波前传感器探测系统中噪声随时间及空间变化频率较快的特点,为了准确估计系统的最优阈值,根据高斯光斑与噪声的分布特性,提出一种以滑动窗口内像素均值及图像信号的局部梯度作为参数,构造关于噪声权重函数的方法,由此获得子孔径阈值的最优估计值,并详细分析了算法的基本原理和实现过程.以典型处理方法获取的阈值与理论最优阈值的误差作为评价标准,仿真和实验结果表明本文提出的阈值估计方法在不同信噪比、不同光斑大小的条件下,均能取得优于典型阈值处理方法获得的结果,且与理论最优阈值的误差小于10%.     

机器学习在紫外法测定硝酸盐氮浓度中的应用

紫外分光光度法(UV法)由于较传统化学方法具有效率高操作简便、无二次污染且可现场原位测试等优点,近些年来被广泛应用到水质参数的测试中。硝酸盐氮是工业废水中的主要污染物之一。基于UV法测量水体中硝酸盐氮浓度的标准方法是分别测量水样在220nm和275nm处的吸光度,然后用275 nm处的吸光度对220 nm处的吸光度进行校正,进而绘制出校正后的吸光度与硝酸盐氮浓度的标准曲线。然而,当硝酸盐氮浓度升高时,标准法所采用的朗伯比尔定律的线性关系以及不同物质吸光度叠加的线性不能很好地满足,在实际的实验测试中也发现,很难建立硝酸盐氮在220 nm处的吸收模型。为了克服单波长或双波长方法的缺陷,将硝酸盐氮吸收峰范围的各个波长的吸光特性引入到模型的建立之中。同时,为了降低模型的复杂度,在建立模型之前先对吸光度数据进行主成分分析,将输入数据的维度数从107压缩到4,然后对压缩后的数据使用局部加权线性回归法建模,该吸收模型对于训练样本和测试样本都有较好的预测结果,且能够适应高浓度时吸光度与浓度的非线性关系,测量上限可达几百mg·L-1。另外,此方法的原理和流程也适用于其他水质参数吸收模型的建立。     

反气相色谱法与Hansen溶解度参数法测定聚乙烯醇溶解度参数及相关热力学性质

采用反气相色谱（IGC）法,以聚乙烯醇（PVA）为固定相,脂肪族、芳香族、醇、酮及卤代烃5类18种化合物为探针分子,研究PVA的溶解性质并获得了PVA在383.15～423.15 K范围内的溶解度参数（δ₂）及相关热力学性质,并与Hansen溶解度参数法（HSP）测得的溶解度参数（δ_T）进行比较。结果表明,5类溶剂对PVA溶解能力的趋势为酮类 >醇类 >卤代烃、芳香类、脂肪族类>脂环族,卤代烃、芳香类和脂肪族类溶剂的溶解能力相似;在测试温度范围内PVA的δ₂随温度升高而增加;采用IGC法外推出室温（298.15 K）下PVA的δ₂为27.69 （J/cm³）^0.5,与HSP法测得室温下PVA的δ_T（27.77 （J/cm³）^0.5）一致。PVA溶解度参数及相关热力学参数的研究为其应用及相关研究提供了定量依据。     

Group inverses for some 2 × 2 block matrices over rings

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA) ^# both exist; (ii) B is invertible and m = n; (iii) A^# and (D - CA^#B)^# both exist, C = CAA^# , where A and D are m × m and n × n matrices, respectively.     

一维热传导方程热源反问题基于最小二乘法的正则化方法

研究一维热传导方程热源反问题.给出基于最小二乘支持向量机（LS-SVM）求解的半解析表达式,此外还给出一种参数调节方法以及算法稳定性的证明.数值实验表明该方法具有较高的数值精度和稳定性.     

Group invertible block matrices

Let M=(ABCD) (A and D are square) be a 2 × 2 block matrix over a skew field, where A is group invertible. Let S=D-CA^#B denote the generalized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions:(1)S=0; (2) S is group invertible and CA^πB=0, where A^π=I-AA^#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215: 132–139]     

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction(NWP). Considering the continuous evolution of the atmosphere, the observed data(ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers’ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.     

应变液晶的负压光效应和反式压光效应

介绍聚合物分散液晶和应变液晶概念,给出聚合物分散液晶调光玻璃的"正压光效应"、"负压光效应"和"反式压光效应"三种效应定义.实验制备出负压光效应和反式压光效应新型应变调光玻璃样品,测试样品散射态雾度90%以上,半透明态透光率接近30%.用偏光显微术研究压光效应原理,表明对样品施加垂面按压或拉伸的应力诱导作用会引起液晶微滴中液晶分子具有某些特殊排列方式,导致样品光学性质发生显著变化.建立垂面拉伸液晶微滴模型,计算模拟所绘出的图形与偏光显微镜照片独特花样十分相似,进而合理解释了实验现象.应变液晶压光效应研究具有聚合物分散液晶基础研究意义和开发非电控调光玻璃的实际应用价值.