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Soft Tissue Deformation Model Based on marquardt algorithm and Enrichment Function

Computer Modeling in Engineering & Sciences 2020年第9期124卷 1131-1147页

作者： Xiaorui Zhang Xuefeng Yu Wei Sun Aiguo Song Jiangsu Engineering Center of Network Monitoring Engineering Research Center of Digital ForensicsMinistry of EducationSchool of Computer and SoftwareNanjing University of Information Science&TechnologyNanjing210044China Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology Nanjing University of Information Science&TechnologyNanjing210044China State Key Laboratory of Bioelectronics Jiangsu Key Lab of Remote Measurement and ControlSchool of Instrument Science and EngineeringSoutheast UniversityNanjing210096China

In order to solve the problem of high computing cost and low simulation accuracy caused by discontinuity of incision in traditional meshless model,this paper proposes a soft tissue deformation model based on the marquardt algorithm and enrichment *** model is based on the element-free Galerkin method,in which Kelvin viscoelastic model and adjustment function are *** algorithm is applied to fit the relation between force and displacement caused by surface deformation,and the enrichment function is applied to deal with the discontinuity in the meshless *** verify the validity of the model,the Sensable Phantom Omni force tactile interactive device is used to simulate the deformations of stomach and *** results show that the proposed model improves the real-time performance and accuracy of soft tissue deformation simulation,which provides a new perspective for the application of the meshless method in virtual surgery.

关键词： Virtual surgery meshless model marquardt algorithm enrichment function soft tissue simulation

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A Joint Optimization of Momentum Item and Levenberg-marquardt algorithm to Level Up the BPNN's Generalization Ability

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-10页

作者： Xiao, Lei Chen, Xiaohui Zhang, Xinghui Chongqing Univ State Key Lab Mech Transmiss Chongqing 400030 Peoples R China Mech Engn Coll Shijiazhuang 050003 Peoples R China

Back propagation neural network (BPNN) as a kind of artificial neural network is widely used in pattern recognition and trend prediction. For standard BPNN, it has many drawbacks such as trapping into local optima, oscillation, and long training time. Because training the standard BPNN is based on gradient descent method, and the learning rate is fixed. Momentum item and Levenberg-marquardt (LM) algorithmare two ways to adjust the weights among the neurons and improve the BPNN's performance. However, there is still much space to improve the two algorithms. The hybrid optimization of damping factor of LM and the dynamic momentum item is proposed in this paper. The improved BPNN is validated by Fisher Iris data and wine data. Then, it is used to predict the visit spend. The database is provided by Dunnhumby's Shopper Challenge. Compared with the other two improved BPNNs, the proposed method gets a better performance. Therefore, the proposed method can be used to do the pattern recognition and time series prediction more effectively.

关键词： marquardt algorithm BACK propagation (Artificial intelligence) NEURAL networks (Computer science) GENERALIZATION PATTERN recognition systems

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Fermentation Process Modeling with Levenberg-marquardt algorithm and Runge-Kutta Method on Ethanol Production by Saccharomyces cerevisiae

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-10页

作者： Liu, Dengfeng Xu, Ling Xiong, Weili Zhang, Hong-Tao Lin, Chi-Chung Jiang, Lihua Xu, Baoguo Jiangnan Univ Minist Educ Key Lab Ind Adv Proc Control Light Ind Wuxi 214122 Peoples R China Wuxi Inst Commerce Sch Internet Things Technol Wuxi 214153 Peoples R China Jiangnan Univ Minist Educ Key Lab Ind Biotechnol Wuxi 214122 Peoples R China

The core of the Chinese rice wine making is a typical simultaneous saccharification and fermentation (SSF) process. In order to control and optimize the SSF process of Chinese rice wine brewing, it is necessary to construct kinetic model and study the influence of temperature on the Chinese rice wine brewing process. An unstructured kinetic model containing 12 kinetics parameters was developed and used to describe the changing of kinetic parameters in Chinese rice wine fermentation at 22, 26, and 30 degrees C. The effects of substrate and product inhibitions were included in the model, and four variable, including biomass, ethanol, sugar and substrate were considered. The R-square values for the model are all above 0.95 revealing that the model prediction values could match experimental data very well. Our model conceivably contributes significantly to the improvement of the industrial process for the production of Chinese rice wine.

关键词： SACCHAROMYCES cerevisiae FERMENTATION marquardt algorithm RUNGE-Kutta formulas ETHANOL

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THE FIT OF POLAR WANDER CURVES BY SMALL CIRCLES USING marquardt algorithm - STATISTICAL PROPERTIES

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GEOPHYSICAL JOURNAL INTERNATIONAL 1991年第3期105卷 731-745页

作者： SCHOTT, JJ TURLOT, JC THOMANN, J INST RECH MATH AVANCES F-67000 STRASBOURGFRANCE CNRS CTR CALCULF-67037 STRASBOURGFRANCE

The method of constructing smooth apparent polar wander paths by fitting to small circle arcs is re-examined. The calculation of the best fitting small circle axis and angle is carried out by means of an iterative, rapidly convergent method. In addition, statistical properties are derived for the various estimated parameters in the linear asymptotic approximation, which allows, in particular, the determination of ellipses of confidence around the calculated poles of the model. Applications to the North American apparent polar wander path using previously published data sets are given as illustrations. In each case, the consistency of the inferred statistics has been checked by simulations.

关键词： LINEAR APPROXIMATION marquardt algorithm POLAR WANDER PATH SMALL CIRCLE FITTING STATISTICAL PROPERTIES

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Levenberg-marquardt algorithm for Mackey-Glass Chaotic Time Series Prediction

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DISCRETE DYNAMICS IN NATURE AND SOCIETY 2014年第1期2014卷 1-6页

作者： Zhao, Junsheng Li, Yongmin Yu, Xingjiang Zhang, Xingfang Liaocheng Univ Sch Math Liaocheng 252059 Peoples R China Huzhou Univ Sch Sci Huzhou 313000 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China

For decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is rapid in the beginning of the learning process, while the convergence speed is very slow when the parameter is near to the minimum point. In order to overcome these problems, we introduce the Levenberg-marquardt algorithm (LMA). Firstly, a rough introduction is given to the multilayer perceptron, including the structure and the model approximation method. Secondly, we introduce the LMA and discuss how to implement the LMA. Lastly, an illustrative example is carried out to show the prediction efficiency of the LMA. Simulations show that the LMA can give more accurate prediction than the gradient descent method.

关键词： marquardt algorithm TIME series analysis MULTILAYER perceptrons LOSS functions (Statistics) TIME delay systems NONLINEAR systems

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Prediction of discharge through a sharp-crested triangular weir using ANN model trained with Levenberg-marquardt algorithm

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MODELING EARTH SYSTEMS AND ENVIRONMENT 2022年第1期8卷 1405-1417页

作者： Ali, Md. Shaheer Ayaz, Md. Mansoor, Talib Aligarh Muslim Univ Univ Polytech Civil Engn Sect Aligarh 202002 Uttar Pradesh India Aligarh Muslim Univ Dept Civil Engn Zakir Husain Coll Engn & Technol Aligarh 202002 Uttar Pradesh India

The measurement of discharge plays an important role in the design of open channels. Direct measurements of discharges in large canals and rivers are not feasible because of high flow. Weirs are the most widely used discharge-measuring device for open channels. In this study, the experimental study along with the modeling of discharge through a sharp-crested triangular weir using ANN model has been conducted. The sharp-crested triangular weirs having apex angles 30 degrees, 45 degrees, 60 degrees, 75 degrees, 90 degrees and weir heights 15 cm, 18 cm, and 20 cm have been used in this study. The experiments were conducted for each combination of weir angle and weir height. The head above the weir crest was measured for all such combinations of apex angles and weir heights for different discharges. These experimental data are then used to train the ANN model to predict the discharge over a sharp-crested triangular weir. The Levenberg-marquardt algorithm has been used as training algorithm. The MSE and R have been used as statistical parameters to judge the performance of ANN model. The ANN model terminates after 18 epochs and the MSE obtained for training, validation and testing are 8.477e - 08, 1.471 e - 07 and 1.325 e - 07, respectively. The corresponding R values obtained for training, validation and testing are 0.9987, 0.9973 and 0.9962, respectively. It was also observed that the predicted discharge stays within the range of +/- 5% of the experimental discharge value. The model performance results are encouraging and conclusive and the developed ANN model may be used to predict the discharge over sharp-crested triangular weir precisely.

关键词： Triangular weir ANN Discharge Open channel flow Levenberg– marquardt algorithm

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Biomolecular Interaction Analysis Using an Optical Surface Plasmon Resonance Biosensor with a marquardt algorithm

Biomolecular Interaction Analysis Using an Optical Surface P...

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3rd International Conference on Photonics and Image in Agriculture Engineering (PIAGENG) - Image Processing and Photonics for Agricultural Engineering

作者： Wei, Wensong Shi, Liang Li, Huiqin Zhu, Chenwen Mu, Linying Hou, Jinbo Wang, Manping Cao, Baiqiong Hu, Jiandong Henan Agr Univ Coll Mech & Elect Engn Zhengzhou 450002 Peoples R China

ISBN: (纸本)9780819495587

This current paper presented the kinetic analysis and model building using the marquardt algorithm based on Gauss-Newton iteration for biomolecular interaction. This algorithm for biomolecular interaction analysis of the optical surface plasmon resonance was applied to implement the nonlinear fitting of association and disassociation process of the receptor to ligand (or the antibody to antigen). Finally, the kinetic parameters were obtained from the fitting curve established by the marquardt algorithm. The results show that the marquardt algorithm does not only reduce the dependence of initial value to avoid the divergence but also can greatly reduce the iterative regression times. The correlation coefficient R-squared of the original curve formed by OriginPro and the fitting curves constructed using the marquardt algorithm in association process and in disassociation process were 0.99158 and 0.99693, respectively. Correspondingly, the kinetic parameters and affinity constants were evaluated using the obtained data from the fitting results.

关键词： surface plasmon resonance biomolecular interaction marquardt algorithm kinetic analysis association and dissociation rate constants

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A simple marquardt algorithm for the nonlinear least-squares problem

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Statistics and Probability Letters 1983年第6期1卷 301-305页

作者： Okamoto, Masashi Ihara, Masamori Department of Applied Mathematics Osaka University Toyonaka Osaka 560 Japan

A new implementation of the marquardt method for the nonlinear least-squares problem is presented. The algorithm is very simple but its performance with nine test functions is at least comparable with either Davidon-F... 详细信息

关键词： marquardt algorithm nonlinear least-squares problem

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Improved marquardt algorithm for Training Neural Networks for Chemical Process Modeling

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Tsinghua Science and Technology 2002年第5期7卷 454-457页

作者：吴建昱何小荣 Department of Chemical Engineering Tsinghua University Beijing 100084 China

Back-propagation (BP) artificial neural networks have been widely used to model chemical processes. BP networks are often trained using the generalized delta-rule (GDR) algorithm but application of such networks is limited because of the low convergent speed of the algorithm. This paper presents a new algorithm incorporating the marquardt algorithm into the BP algorithm for training feedforward BP neural networks. The new algorithm was tested with several case studies and used to model the Reid vapor pressure (RVP) of stabilizer gasoline. The new algorithm has faster convergence and is much more efficient than the GDR algorithm.

关键词： neural network marquardt algorithm training

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Real-time deformation of human soft tissues: A radial basis meshless 3D model based on marquardt's algorithm

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COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2018年 153卷 237-252页

作者： Zhou, Jianyong Luo, Zu Li, Chunquan Deng, Mi Nanchang Univ Sch Mechatron Engn Nanchang Jiangxi Peoples R China Nanchang Univ Sch Informat Engn Nanchang Jiangxi Peoples R China New Mexico State Univ Dept Math Sci Las Cruces NM 88003 USA

Background: When the meshless method is used to establish the mathematical-mechanical model of human soft tissues, it is necessary to define the space occupied by human tissues as the problem domain and the boundary of the domain as the surface of those tissues. Nodes should be distributed in both the problem domain and on the boundaries. Under external force, the displacement of the node is computed by the meshless method to represent the deformation of biological soft tissues. However, computation by the meshless method consumes too much time, which will affect the simulation of real-time deformation of human tissues in virtual surgery. Methods: In this article, the marquardt's algorithm is proposed to fit the nodal displacement at the problem domain's boundary and obtain the relationship between surface deformation and force. When different external forces are applied, the deformation of soft tissues can be quickly obtained based on this relationship. Results and conclusions: The analysis and discussion show that the improved model equations with marquardt's algorithm not only can simulate the deformation in real-time but also preserve the authenticity of the deformation model's physical properties. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Meshless method marquardt algorithm Surface fitting Virtual surgery Real-time deformation

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