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Monitoring and diagnosis of complex production process based on free energy of Gaussian–Bernoulli restricted Boltzmann machine

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Journal of Iron and Steel Research(International) 2023年第5期30卷 971-984页

作者： Qian-qian Dong Qing-ting Qian Min Li Gang Xu Collaborative Innovation Center of Steel Technology University of Science and Technology BeijingBeijing 100083China

Online monitoring and diagnosis of production processes face great challenges due to the nonlinearity and multivariate of complex industrial processes.Traditional process monitoring methods employ kernel function or multilayer neural networks to solve the nonlinear mapping problem of data.However,the above methods increase the model complexity and are not interpretable,leading to difficulties in subsequent fault recognition/diagnosis/location.A process monitoring and diagnosis method based on the free energy of Gaussian-Bernoulli restricted Boltzmann machine(GBRBM-FE)was proposed.Firstly,a GBRBM network was established to make the probability distribution of the reconstructed data as close as possible to the probability distribution of the raw data.On this basis,the weights and biases in GBRBM network were used to construct F statistics,which represents the free energy of the sample.The smaller the energy of the sample is,the more normal the sample is.Therefore,F statistics can be used to monitor the production process.To diagnose fault variables,the F statistic for each sample was decomposed to obtain the Fv statistic for each variable.By analyzing the deviation degree between the corresponding variables of abnormal samples and normal samples,the cause of process abnormalities can be accurately located.The application of converter steelmaking process demonstrates that the proposed method outperforms the traditional methods,in terms of fault monitoring and diagnosis performance.

关键词： Process monitoring Fault diagnosis Gaussian–Bernoulli restricted Boltzmann machine energy function free energy Converter steelmaking production process

Numerical Simulation of the Distribution Function and free energy of a Single Wormlike Polymer Confined between Hard Walls

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Chinese Journal of Polymer Science 2020年第2期38卷 179-186,I0007页

作者： Yang Gu Hui Zhang Dong-Liang Zhang School of Mathematics Sciences Beijing Normal UniversityBeijing 100875China Laboratory of Mathematics and Complex Systems Ministry of EducationSchool of Mathematics SciencesBeijing Normal UniversityBeijing 100875China The department of Orthodontics Beijing Stomatology Hospital Affiliated to Capital Medical UniversityBeijing 100006China

We focus on the distribution and free energy of a wormlike polymer confined between two parallel hard walls.The variation in the distribution and free energy of the wormlike chain as the spacing between the walls decreases(or as the total contour length of the wormlike chain increases or as the persistence length of the chain increases)is simulated.The main reason for these changes is a degradation of the long wormlike chain into a Gaussian long chain under weak confinement.

关键词： Wormlike polymer free energy Weak confinement

Calculation of free energy of the Integrable Landau—Lifshitz model

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Chinese Physics Letters 2003年第7期20卷 1009-1012页

作者：蔡从中王万录陈宇综 DepartmentofAppliedPhysics ChongqingUniversityChongqing400044 DepartmentofComputationalScience NationaluniversityofSingaporeSingapore117543 DepartmentofAppliedPhysics ChongqingUniversityChongqing400044 DepartmentofComputationalScience NationaluniversityofSingaporeSingapore117543

The generalized Bethe-ansatz method of thermodynamic analysis of integrable systems was employed to compute the free energy of a classical integrable model, i.e., the Landau-Lifshitz model. Using the action-angle variables of the model and by imposing a periodic boundary condition, we derive a phase-shifted density of states for the excitations of the system. The free energy, in the thermodynamic limit, can be expressed analytic in terms of two coupled nonlinear integral equations of the finite temperature excited energy for effective phonons and kinks (antikinks). We solve these equations iteratively for a special case that the model is in the limit of anisotropic strong yz coupling.

关键词： free energy

A Cluster Expansion free Method for Computing Higher Derivatives of the free energy and Estimating the Error between the Finite and Infinite Volume free energy

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Journal of Applied Mathematics and Physics 2022年第5期10卷 1762-1784页

作者： Assane Lo University of Wollongong Dubai and Wollongong Australia

The theory of phase transitions is one of the branches of statistical physics in which smoothness and continuity play an important role. In fact, phase transitions are characterized mathematically by the degree of non-analyticity of the thermodynamic potentials associated with the given system. In this paper, we propose a method that is not based on cluster expansions for computing the higher derivatives of the free energy and estimating the error between the finite and infinite volume free energy in certain continuum gas models. Our approach is suitable for a direct proof of the analyticity of the pressure or free energy in certain models of Kac-type. The methods known up to now strongly rely on the validity of the cluster expansion. An extension of the method to classical lattice gas models is also discussed.

关键词： Witten Laplacians Analyticity free energy Kac-Models

A Study on the Standard free energy of Formation of LaNi_5 and CeNi_5

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Journal of Rare Earths 1993年第1期11卷 28-31页

作者：肖理生于化龙王常珍徐秀光 Department Physicochemistry of Metallurgy Northeast University of TechnologyShenyang 110006China

关键词： LaNi_5 CeNi_5 Thermodynamics free energy

Study on Surface free energy of Thermochromic Wood

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Chinese Forestry Science and Technology 2010年第1期9卷 60-66页

作者： LIU Zhijia FU Feng BAO Fucheng Research Institute of Wood Industry, Chinese Academy of Forestry, Beijing 100091, P.R.China

Thermochromic wood is a kind of new functional materials. It is significant for thermochromic wood development to study surface free energy. Samples of Chinese white poplar were colored using thermochromic agent though the method of ultrasonic impregnation and its surface free energy was investigated in the experiment. The results showed that the surface free energy for untreated, black-red, orange-yellow and blue thermochromic wood was 40.25, 29.85, 28.30 and 21.05 mN/m, respectively. The FTIR results showed that both the type and the number of function groups resulted in the change of free energy for untreated and thermochromic wood.

关键词： thermochromic wood free energy function group contact angle

Contribution of Disclination Lines to free energy of 2-Dimensional Liquid Crystals in Single-Elastic Constant Approximation

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Journal of Shanghai University(English Edition) 2004年第2期8卷 155-158页

作者：王玉生张慧杨国宏 Department of Physics Department of Chemistry

In light of the φ-mapping method, the contribution of disclination lines to the free energy density of 2-dimensional liquid crystals is studied in the single-elastic constant approximation. It is pointed out that, compared with the previous theory, the free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of the disclination lines themselves which is centralized at the disclination lines and topoligically quantized in a unit of 1/2kπ. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e., the disclination strength. From the method of Lagrangian multipliers, the equilibrium equation and the molecular field of 2-dimensional liquid crystals are also obtained. It is shown that the physical meaning of the Lagrangian multiplier is just the distorted energy density. Key words director field - disclination line - free energy - Lagrangian multiplier PASC2001 64.70.Md - 02.40.-k

关键词： director field disclination line free energy Lagrangian multiplier

Sequence and thermodynamic characteristics of terminators revealed by FlowSeq and the discrimination of terminators strength

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Synthetic and Systems Biotechnology 2022年第4期7卷 1046-1055页

作者： Weiji Zhai Yanting Duan Xiaomei Zhang Guoqiang Xu Hui Li Jinsong Shi Zhenghong Xu Xiaojuan Zhang Biotechnology of Ministry of Education School of BiotechnologyJiangnan UniversityWuxiChina National Engineering Research Center for Cereal Fermentation and Food Biomanufacturing Jiangnan UniversityWuxiChina School of Life Science and Health Engineering Jiangnan UniversityWuxi214122China Jiangsu Provincial Engineering Research Center for Bioactive Product Processing Jiangnan University1800 Lihu AvenueWuxi214122China

The intrinsic terminator in prokaryotic forms secondary RNA structure and terminates the transcription.However,leaking transcription is common due to varied terminator strength.Besides of the representative hairpin and U-tract structure,detailed sequence and thermodynamic features of terminators were not completely clear,and the effect of terminator on the upstream gene expression was unclearly.Thus,it is still challenging to use terminator to control expression with higher precision.Here,in E.Coli,we firstly determined the effect of the 3′-end sequences including spacer sequences and terminator sequences on the expression of upstream and downstream genes.Secondly,terminator mutation library was constructed,and the thermodynamic and sequence features differing in the termination efficiency were analyzed using the FlowSeq technique.The result showed that under the regulation of terminators,a negative correlation was presented between the expression of upstream and downstream genes(r=􀀀0.60),and the terminators with lower free energy corelated with higher upstream gene expression.Meanwhile,the terminator with longer stem length,more compact loop and perfect U-tract structure was benefit to the transcription termination.Finally,a terminator strength classification model was established,and the verification experiment based on 20 synthetic terminators indicated that the model can distinguish strong and weak terminators to certain extent.The results help to elucidate the role of terminators in gene expression,and the key factors identified are crucial for rational design of terminators,and the model provided a method for terminator strength prediction.

关键词： Intrinsic terminator Transcription termination Machine learning Structure-activity relationship FlowSeq free energy

A novel bird-nest-like air superoleophobic/superhydrophilic Cu(OH)2-based composite coating for efficient oil–water separation

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Frontiers of Materials Science 2022年第2期16卷 167-179页

作者： Zhiwei ZENG Xinzhu WU Yan LIU Lulu LONG Bo WANG Lilin WANG Gang YANG Xiaohong ZHANG Fei SHEN Yanzong ZHANG College of Environmental Sciences Sichuan Agricultural UniversityChengdu 611130China Beijing Municipal Road&Bridge Co. Ltd.Beijing 100045China

An air superoleophobic/superhydrophilic composite coating with a unique structure was fabricated by oxidation and further modification of the copper mesh,and its design principle was clarified.This unique bird-nest-like configuration gives it instant superhydrophilicity due to the high surface roughness and high polar surface free energy components,while air superoleophobicity is caused by its extremely low dispersive surface free energy components.Furthermore,a water-resistance mechanism was proposed whereby a polyelectrolyte plays a critical role in improving the water-resistance of fluorosurfactants.It can separate oil–water mixtures with high efficiency(98.72%)and high flux(25185 L·m−2·h−1),and can be reused.In addition,our composite coating had certain anti-acid,anti-alkali,anti-salt and anti-sand impact performance.More importantly,after being soaked in water for a long time or being exposed to the air for a long time,it still retained ultra-high air oil contact angle and showed excellent stability,which provided the possibility for practical applications.Thus,these findings offer the potential for significant practical applications in managing oily wastewater and marine oil spill incidents.

关键词： dispersion force surface tension free energy water resistance oily wastewater