Output-relevant Variational autoencoder for Just-in-time soft sensor modeling with missing data

Main challenges for developing data-based models lie in the existence of high-dimensional and possibly missing observations that exist in stored data from industry process. Variational autoencoder (VAE) as one of the deep learning methods has been applied for extracting useful information or features from high-dimensional dataset. Considering that existing VAE is unsupervised, an output-relevant VAE is proposed for extracting output-relevant features in this work. By using correlation between process variables, different weight is correspondingly assigned to each input variable. With symmetric Kullback–Leibler (SKL) divergence, the similarity is evaluated between the stored samples and a query sample. According to the values of the SKL divergence, data relevant for modeling are selected. Subsequently, Gaussian process regression (GPR) is utilized to establish a model between the input and the corresponding output at the query sample. In addition, owing to the common existence of missing data in output data set, the parameters and missing data in the GPR are estimated simultaneously. A practical debutanizer industrial process is utilized to illustrate the effectiveness of the proposed method.     

Mixture ratio modeling of dynamic systems

Any knowledge extraction relies (possibly implicitly) on a hypothesis about the modelled-data dependence. The extracted knowledge ultimately serves to a decision-making (DM). DM always faces uncertainty and this makes probabilistic modelling adequate. The inspected black-box modeling deals with “universal” approximators of the relevant probabilistic model. Finite mixtures with components in the exponential family are often exploited. Their attractiveness stems from their flexibility, the cluster interpretability of components and the existence of algorithms for processing high-dimensional data streams. They are even used in dynamic cases with mutually dependent data records while regression and auto-regression mixture components serve to the dependence modeling. These dynamic models, however, mostly assume data-independent component weights, that is, memoryless transitions between dynamic mixture components. Such mixtures are not universal approximators of dynamic probabilistic models. Formally, this follows from the fact that the set of finite probabilistic mixtures is not closed with respect to the conditioning, which is the key estimation and predictive operation. The paper overcomes this drawback by using ratios of finite mixtures as universally approximating dynamic parametric models. The paper motivates them, elaborates their approximate Bayesian recursive estimation and reveals their application potential.     

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, II: Minimization of ∇·B Numerical Error

An adaptive numerical dissipation control in a class of high order filter methods for compressible MHD equations is systematically discussed. The filter schemes consist of a divergence-free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Some of these filter variants provide a natural and efficient way for the minimization of the divergence of the magnetic field (∇·B) numerical error in the sense that commonly used divergence cleaning is not required. Numerical experiments presented emphasize the performance of the ∇·B numerical error. Many levels of grid refinement and detailed comparison of the filter methods with several commonly used compressible MHD shock-capturing schemes will be illustratedA condensed version appears in the Proceedings of the International Conference on High Performance Scientific Computing, March 10-14, 2003, Hanoi, Vietnam. This is a revised version of a longer internal report, Feb. 19, 2004. The longer internal report was published as a RIACS Technical Report TR03.10, July 2003, NASA Ames Research Center     

激光二极管线阵光束变换研究

推导出激光二极管线阵光束通过透镜系统的光强分布表达式，分析了出射光束的传输特性，设计一种凹柱透镜的光束变换系统得到一维均匀光强分布。此外，给出扩展角宽度的计算公式。     

Gelfand-Yaglom-Perez theorem for generalized relative entropy functionals

The measure-theoretic definition of Kullback-Leibler relative-entropy (or simply KL-entropy) plays a basic role in defining various classical information measures on general spaces. Entropy, mutual information and conditional forms of entropy can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. These measure-theoretic definitions are key to extending the ergodic theorems of information theory to non-discrete cases. A fundamental theorem in this respect is the Gelfand-Yaglom-Perez (GYP) Theorem [M.S. Pinsker, Information and Information Stability of Random Variables and Process, 1960, Holden-Day, San Francisco, CA (English ed., 1964, translated and edited by Amiel Feinstein), Theorem. 2.4.2] which states that measure-theoretic relative-entropy equals the supremum of relative-entropies over all measurable partitions. This paper states and proves the GYP-theorem for Rényi relative-entropy of order greater than one. Consequently, the result can be easily extended to Tsallis relative-entropy.     

Inferencia bayesiana en mixturas: metodos aproximados

Resumen últimamente se ha dedicado una gran atención a las técnicas de aproximación de mixturas de distribuciones. En este trabajo se consideran problemas de estimación de los parámetros de mezcla en una mixtura finita, desde una metodología bayesiana, que conducen a problemas de aproximación de mixturas finitas y se proponen dos nuevos métodos de aproximación. Bajo ciertas condiciones se demuestra que ambos métodos son asintóticamente equivalentes a un tercer método, de aplicación mucho más sencilla. El trabajo se concluye con un estudio de simulación en el que se analiza la bondad de los métodos de aproximación que aquí se exponen.      

Distributions most nearly compatible with given families of conditional distributions

Consider a discrete bivariate random variable (X, Y) with possible values 1, 2, ...,I forX and 1, 2, ...J forY. Suppose that putative families of conditional distributions, forX given values ofY and ofY given values ofX, are available. After reviewing conditions for compatibiity of such conditional specifications of the distribution of (X, Y), attention is focussed on the incompatible case. The Kullback-Leibler information function is shown to provide a convenient measure of inconsistency. Using it, algorithms are provided for computing the joint distribution for (X, Y) that is least discrepant from the given inconsistent conditional specifications. Other discrepancy measures are briefly discussed.     

双轴旋转惯导系统误差传播特性分析

针对双轴旋转惯导系统的误差传播特性问题,推导出双轴旋转惯导系统的误差方程,通过特征值判据证明了误差方程在李雅普诺夫意义下的稳定性,设计了一种合理的十六次序转位方案,建立了研究误差传播特性的方法,分别仿真了初始对准误差角、陀螺常值漂移、陀螺安装误差、陀螺标度因数误差4种因素对导航误差传播特性的影响。结果表明,4种误差因素大小均与导航误差大小成线性关系,并且满足叠加性;4种误差因素会引起导航姿态、导航速度、导航纬度的常值误差和振荡误差,但不会引起积累误差;陀螺标度因数误差会引起导航经度误差的积累和发散。最后提出了减小双轴旋转惯导系统导航误差的措施,对设计双轴旋转惯导系统有一定的参考价值。     

核空间散度阈值法

提出了一种核空间散度阈值分割方法。首先定义了一种参数型Bregman散度;其次提出了参数型Bregman散度阈值法,并将现有交叉熵阈值法和Otsu阈值法统一起来;再次基于参数型Bregman散度构造了核空间中一种新的不对称核函数,将图像灰度级从欧氏空间变换到再生核空间,获得了一种核空间的散度阈值分割法;最后研究了该分割法中核函数参数选取方法。实验结果表明,基于核空间的散度分割法具有一定的普适性,并能改善现有交叉熵阈值法和Otsu阈值法的分割性能,同时也可将这两种经典阈值分割法看做核空间散度阈值法的特殊情形。     

Analysis of Sequence Divergence in Mammalian ABCGs Predicts a Structural Network of Residues That Underlies Functional Divergence

The five members of the mammalian G subfamily of ATP-binding cassette transporters differ greatly in their substrate specificity. Four members of the subfamily are important in lipid transport and the wide substrate specificity of one of the members, ABCG2, is of significance due to its role in multidrug resistance. To explore the origin of substrate selectivity in members 1, 2, 4, 5 and 8 of this subfamily, we have analysed the differences in conservation between members in a multiple sequence alignment of ABCG sequences from mammals. Mapping sets of residues with similar patterns of conservation onto the resolved 3D structure of ABCG2 reveals possible explanations for differences in function, via a connected network of residues from the cytoplasmic to transmembrane domains. In ABCG2, this network of residues may confer extra conformational flexibility, enabling it to transport a wider array of substrates.