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An Almost Sure Result on Approximation of Homogeneous Random Field from Local Averages

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Chinese Journal of Electronics 2019年第1期28卷 93-99页

作者： song zhanjie ZHANG Shuo School of Mathematics Tianjin University Department of Mathematics Tianjin University of Finance and Economics

The problem of approximation of homogeneous random field from asymmetric local average sampling is considered in this paper. As a general sampling result, a sufficient condition is obtained to ensure the homogeneous random field be approximated from local averages with probability 1, which extended the result for weak sense stochastic process from local averages to homogeneous random field.

关键词： Sampling theorem Homogeneous random field Local averages sampling

Improved Quality Prediction Model for Multistage Machining Process Based on Geometric Constraint Equation

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Chinese Journal of Mechanical Engineering 2016年第2期29卷 430-438页

作者： ZHU Limin HE Gaiyun song zhanjie Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education Tianjin University School of Science Tianjin University

Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.

关键词： quality prediction variation reduction geometric constraint equation deviation matrix multistage machining process

Optimal query error of quantum approximation on some Sobolev classes

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Science China Mathematics 2008年第9期51卷 1664-1678页

作者： song zhanjie YE PeiXin School of Sciences Tianjin UniversityTianjin 300072China School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071China School of Electronic Information Engineering Tianjin UniversityTianjin 300072China

We study the approximation of the imbedding of functions from anisotropic and generalized Sobolev classes into L q ([0, 1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from L p N to L q N , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(W p r ([0, 1] d )) to L q ([0, 1] d ) space for all 1 ? q,p ? ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

关键词： quantum approximation Sobolev classes n-th minimal query error 41A63 65D15

Multivariate spectral estimation based on THREE

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The Journal of China Universities of Posts and Telecommunications 2015年第4期22卷 26-32页

作者： Li Ying Wang Jian song zhanjie School of Science Tianjin University National Ocean Technology Center Institute of TV and Image Information Tianjin University

Power spectrum estimation is to use the limited length of data to estimate the power spectrum of the signal. In this paper, we study the recently proposed tunable high-resolution estimator（THREE）, which is based on the best approximation to a given spectrum, with respect to different notions of distance between power spectral densities. We propose and demonstrate a different distance for the optimization part to estimate the multivariate spectrum. Its effectiveness is tested through Matlab simulation. Simulation shows that our approach constitutes a valid estimation procedure. And we also demonstrate the superiority of the method, which is more reliable and effective compared with the standard multivariate identification techniques.

关键词： multivariate spectral estimation convex optimization THREE matricial Newton method Matlab simulation

ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

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Acta Mathematica Scientia 2024年第5期44卷 1984-1996页

作者： zhanjie song Jiaxing ZHANG Georgia Tech Shenzhen Institute Tianjin UniversityShenzhen518055China Tianjin Key Laboratory of Brain-Inspired Intelligence Technology Tianjin300072China School of Mathematics Tianjin UniversityTianjin300354China

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random *** estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space *** can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of *** addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

关键词： differential entropy stationary ergodicity space-time random field time series

Nonlocally Centralized Simultaneous Sparse Coding

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Transactions of Tianjin University 2016年第5期22卷 403-410页

作者： Lei Yang song zhanjie School of Electronic Information Engineering Tianjin University School of Sciences Tianjin University

The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlocal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NCSSC)is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image restoration methods.

关键词： sparse representation image restoration low-rank approximation alternative direction method

An Improved Measurement Uncertainty Calculation Method of Profile Error for Sculptured Surfaces

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Chinese Journal of Mechanical Engineering 2019年第6期32卷 154-163页

作者： Chenhui Liu zhanjie song Yicun Sang Gaiyun He Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education Tianjin UniversityTianjin 300350China School of Mathematics Tianjin UniversityTianjin 300350China

The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.

关键词： Second-order GUMM Adaptive Monte Carlo method Uncertainty Converge factor

Pseudo-Multispectral Pedestrian Detection with Deep Thermal Feature Guidance

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Guidance,Navigation and Control 2024年第3期4卷 92-107页

作者： Fuchen Chu Yanwei Pang Xuebin Sun Jiale Cao zhanjie song School of Electrical and Information Engineering Tianjin University Shanghai Artificial Intelligence Laboratory School of Mathematics Tianjin University

With complementary multi-modal information(i.e. visible and thermal), multispectral pedestrian detection is essential for around-the-clock applications, such as autonomous driving, video surveillance, and vicinagearth security. Despite its broad applications, the requirements for expensive thermal device and multi-sensor alignment limit the utilization in real-world applications. In this paper, we propose a pseudo-multispectral pedestrian detection(called Pseudo MPD) method,which employs the gray image converted from the RGB image to replace the real thermal image,and learns the pseudo-thermal feature through deep thermal feature guidance(TFG). To achieve this goal, we first introduce an image base-detail decomposition(IBD) module to decompose image information into base and detail parts. Afterwards, we design a base-detail hierarchical feature fusion(BHFF) module to deeply exploit the information between these two parts, and employ a TFG module to guide pseudo-thermal base and detail feature learning. As a result, our proposed method does not require the real thermal image during inference. The comprehensive experiments are performed on two public multispectral pedestrian datasets. The experimental results demonstrate the effectiveness of our proposed method.

关键词： base-detail hierarchical fusion image decomposition Multispectral pedestrian detection thermal feature guidance vicinagearth security

Discriminative Structured Dictionary Learning for Image Classification

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Transactions of Tianjin University 2016年第2期22卷 158-163页

作者：王萍兰俊花臧玉卫宋占杰 School of Sciences Tianjin University Tianjin Tendbeyond Science and Technology Development Co. Ltd

In this paper, a discriminative structured dictionary learning algorithm is presented. To enhance the dictionary's discriminative power, the reconstruction error, classification error and inhomogeneous representation error are integrated into the objective function. The proposed approach learns a single structured dictionary and a linear classifier jointly. The learned dictionary encourages the samples from the same class to have similar sparse codes, and the samples from different classes to have dissimilar sparse codes. The solution to the objective function is achieved by employing a feature-sign search algorithm and Lagrange dual method. Experimental results on three public databases demonstrate that the proposed approach outperforms several recently proposed dictionary learning techniques for classification.

关键词： sparse representation dictionary learning sparse coding image classification