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The 2013 3rd International Conference on Photonics and Image in Agriculture Engineering (PIAGENG 2013)

作者： Wensong Wei Liang Shi Huiqin Li Chenwen Zhu Linying Mu Jinbo Hou Manping Wang Baiqiong Cao Jiandong Hu College of Mechanical and Electrical Engineering Henan Agricultural University Henan Nongda Xunjie measurement technology co. ltd

ISBN: (纸本)9780819495587

This current paper presented the kinetic analysis and model building using the marquardt algorithm based on GaussNewton 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 Origin Pro 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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Comparative study of kinetic modeling for the oxidative coupling of methane by genetic and marquardt algorithms

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Journal of Natural Gas Chemistry 2010年第3期19卷 293-299页

作者： Shahrnaz Mokhtari Ali Vatani Nastaran Razmi Farooji Iran Polymer and Petrochemical Institute Faculty of Engineering university of Tehran

Overall kinetic studies on the oxidative coupling of methane,OCM,have been conducted in a tubular fixed bed reactor,using perovskite titanate as the reaction *** appropriate operating conditions were found to be：temperature 750-775 ℃,total feed flow rate of 160 ml/min,CH4 /O2 ratio of 2 and GHSV of 100·min-1 .Under these conditions,C 2 yield of 28% was *** of the kinetic data have been performed with lumped rate equations for C2 and COx formation as functions of temperature,O2 and CH4 partial *** models have been selected among the common lumped kinetic *** selected models have been regressed with the experimental data which were obtained from the Catatest system by genetic algorithm in order to obtain optimized *** kinetic coefficients in the overall reactions were optimized by different numerical optimization methods such as：the Levenberg-marquardt and genetic algorithms and the results were compared with one *** has been found that the Santamaria model is in good agreement with the experimental *** Arrhenius parameters of this model have been obtained by linear *** should be noted that the marquardt algorithm is sensitive to the first guesses and there is possibility to trap in the relative minimum.

关键词： oxidative coupling of methane kinetics perovskite genetic algorithm marquardt algorithm

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Gravity anomalies of 2.5-D multiple prismatic structures with variable density: A marquardt inversion

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PURE AND APPLIED GEOPHYSICS 2006年第1期163卷 229-242页

作者： Chakavarthi, V Sundararajan, N Natl Geophys Res Inst Hyderabad 500007 Andhra Pradesh India Osmania Univ Ctr Explorat Geophys Hyderabad 500007 Andhra Pradesh India

We present an inversion technique based on the marquardt algorithm to estimate the depth of a 2.5-D sedimentary basin in addition to the regional gravity anomaly that is associated with the residual gravity anomaly, wherein the density contrast varies parabolically with depth. Forward modeling is carried out through a derived analytical gravity expression of a 2.5-D vertical prism. Inversion of a theoretical gravity anomaly with and without a regional gravity anomaly illustrates the procedure that it is found to be insensitive to the regional gravity effect. Furthermore, the algorithm is exemplified with the gravity anomalies of the derived density-depth model of the Godavari subbasin, India with a parabolic density profile resulting in a more consistent geological model rather than a constant density profile. The main advantage of this method is that it works well even when the profile of interpretation does not bisect the strike length of the sedimentary basin.

关键词： bravity anomalies regional gravity marquardt algorithm 2.5-D gravity inversion Godavari subbasin

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Estimation of empirical coefficients of a granular filtration model

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WATER RESEARCH 1997年第5期31卷 1083-1091页

作者： Dharmappa, HB Prasanthi, H Krishna, MU Xiao, Y UNIV TECHNOL SYDNEY SCH CIVIL ENGNSYDNEYNSW 2007AUSTRALIA ASIAN INST TECHNOL ENVIRONM ENGN PROGRAMBANGKOK 10501THAILAND

In this paper a methodology comprising a non-linear least-squares algorithm for determining the empirical parameters of a filtration model is presented and is rested against literature data. Through the case study it is found that incorporation of a multiplication factor for the sum of the square of errors associated with effluent quality could lead to a more balanced estimation of parameters, while achieving a better fit for both effluent quality and headless. In the case study it is found that the shape of the fitted effluent quality curve has significant impact on the values of the model parameters. The proposed algorithm appears to be well suited for obtaining the best fit for both effluent quality and headless, simultaneously. The value of the multiplication factor should be fixed based on the accuracy required under both effluent quality and headless predictions. The model parameters predicted under each of the case studies, correlated well with the experimental observations. (C) 1997 Elsevier Science Ltd.

关键词： filtration modelling marquardt algorithm particle separation

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Learning nonlinear dynamics with behavior ordinary/partial/system of the differential equations: looking through the lens of orthogonal neural networks

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 2期38卷 1635-1654页

作者： Omidi, M. Arab, B. Rasanan, A. H. Hadian Rad, J. A. Parand, K. Shahid Beheshti Univ Fac Math Sci Dept Comp Sci Tehran Iran Shahid Beheshti Univ Inst Cognit & Brain Sci Dept Cognit Modeling Tehran Iran Inst Res Fundamental Sci IPM Sch Comp Sci Tehran Iran Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON Canada

Applications of neural network algorithms have been grown in recent years and various architectures have been introduced by researchers for the purpose of solving different types of differential equations. Physics informed neural networks, functional link neural networks, and feed-forward differential equation neural networks are some of these architectures. In this paper, we introduce a new neural network for simulating the behavior of Emden-Fowler-type dynamic modeled as an ordinary/partial/system of differential equation, i.e. ODE/PDE/SDE which is based on the development of two introduced functional link neural network and feed-forward differential equation neural network for the partial/system of differential equations. This algorithm uses roots of shifted Chebyshev polynomials as a training data set and the The Levenberg-marquardt algorithm is taken as an optimizer. To show the applicability of the proposed network, it is applied to some test problems and the obtained results are compared with some other neural network approaches and also, some other numerical algorithms. The reported results showed that the algorithm proposed in this paper is a powerful method for simulating the behavior of partial and system of differential equations and is more accurate than other methods in the literature.

关键词： Lane– Emden-type equations Feed-forward neural network Functional link neural network Levenberg– marquardt algorithm Partial differential equations System of differential equations Chebyshev polynomial

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Direct calculation formulas for normal depths of four kinds of parabola-shaped channels

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FLOW MEASUREMENT AND INSTRUMENTATION 2019年 65卷 180-186页

作者： Dai, Shubing Ma, Yulei Jin, Sheng Dalian Univ Technol Sch Hydraul Engn Dalian 116024 Peoples R China

Channels with parabola-shaped cross-section are widely used in water conservancy and hydropower engineering, agricultural irrigation and drainage engineering, so it is necessary to determine the accurate normal depth values for design of open channels, operation management and analysis of gradually varied flow. However, the governing equations are nonintegrable for cubic and semi-quintic parabola-shaped channels in terms of the wetted perimeters. In this study, the Simpson's numerical integral method is introduced to approximate the two nonintegrable wetted perimeters for cubic and semi-quintic parabola-shaped channels which can meet the requirements of engineering design well in the commonly using range of engineering. Subsequently, the approximate wetted perimeters are substituted into the uniform flow equation and the uniform flow equation deforms optimal model identically. The optimal model parameters are determined by the 1stOpt software based on marquardt algorithm and two explicit calculation formulas for the normal depths of cubic and semi-quintic channels are proposed. At the same time, two direct calculation formulas for normal depths of semi-cubic and quadratic parabola-shaped channels are presented as well. Four sets of formulas for normal depths of parabola-shaped channels are presented and their maximum relative errors are 0.52%, - 0.37%, - 0.22% and 0.57%, respectively, which have wide range of application, high precision, concise form and can provide some better guidance for engineering design and operation management.

关键词： Direct calculation formulas Normal depths Parabola-shaped channels Wetted perimeters Simpson's numerical integral method 1stOpt software marquardt algorithm

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Numerical simulation and neural network model for hydromagnetic nanofluid convection in a porous wavy channel with thermal non-equilibrium model

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PHYSICA SCRIPTA 2024年第11期99卷 115219-115219页

作者： Rani, H. P. Shilpa, B. Leela, V Reddy, R. Gangadhara Natl Inst Technol Dept Math Warangal India Dayananda Sagar Coll Engn Dept Math Bangalore India PES Univ Dept Sci & Humanities Bangalore India VTU AMC Engn Coll Dept Math Bangalore India

The present study aims to analyze the nanofluid MHD convective heat transfer in a porous wavy channel with a local thermal non-equilibrium (LTNE) model. Such a model finds applications related to enhancement in thermal performance, increasing the heat transfer coefficient in the compact design of heat exchangers for the aerospace and automotive industries and elevation in the efficiency of the solar collector. A sinusoidal porous wavy LTNE channel containing nanofluid and subjected to the induced and applied magnetic fields is considered. A uniform magnetic field is applied orthogonal to the channel and the induced magnetic field effects are considered due to the large magnetic Reynolds number. The momentum, continuity, energy, and nanoparticle volume fraction equations constitute the coupled nonlinear system of differential equations and are solved using the Galerkin finite element method. The reliability of the technique is assessed by comparing the proposed procedure with the results from earlier sources. A detailed analysis is presented to determine the effects of different physical parameters arising in the system on temperature, nanoparticle concentration, and velocity profiles. As an illustration, the findings exhibit that increasing the modified diffusivity ratio increases the values of the nanoparticle volume fraction whereas, reducing the modified diffusivity ratio enhances the temperature distribution. A higher value of thermal Rayleigh number presents a significant involvement of buoyancy forces, potentially resulting in the development of convective currents. A higher Nield number indicates more effective heat transport from the solid surface to the nanofluid. Consequently, there is a minimal thermal difference between the solid surface and the bulk nanofluid. Effective heat transmission enhances the nanofluid ability to absorb heat and generates a more consistent dispersion of temperature inside the fluid. The performance of the designed algorithms of

关键词： nanofluid convection local thermal non-equilibrium magnetohydrodynamics induced magnetic field Galerkin finite element analysis levenberg marquardt algorithm

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Solving ordinary differential equations using an optimization technique based on training improved artificial neural networks

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SOFT COMPUTING 2021年第5期25卷 3713-3723页

作者： Li, Shangjie Wang, Xingang Northeastern Univ Sch Mech Engn & Automat Shenyang 110819 Peoples R China Northeastern Univ Res Ctr Mech Kinet & Reliabil Qinhuangdao 066004 Hebei Peoples R China

The solution of ordinary differential equations (ODEs) arises in a wide variety of engineering problems. This paper presents a novel method for the numerical solution of ODEs using improved artificial neural networks (IANNs). In the first step, we derive an approximate solution of ODEs by artificial neural networks (ANNs). Then, we construct a joint cost function of network system, it consists of several error functions corresponding to different sample points, and we reformulate Levenberg-marquardt (RLM) algorithm to adjust the network parameters. The advantages of this method are high calculation accuracy and fast convergence speed compared with other existed methods, also increasing the simulation stability of ANNs method. The performance of the new proposed method in terms of calculation accuracy and convergence speed is analyzed for several different types of nonlinear ODEs.

关键词： Differential equations Improved artificial neural networks Joint cost function Reformulate Levenberg– marquardt algorithm

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Hierarchical fractional-order Hammerstein system identification

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2021年第12期52卷 2505-2517页

作者： Marzougui, Soumaya Atitallah, Asma Bedoui, Saida Abderrahim, Kamel Univ Gabes Natl Engn Sch Gabes Res Lab Numer Control Ind Proc Gabes Tunisia

For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and the intermediate variable and the states are unmeasurable. To overcome this difficulty, we transform the system from an input nonlinear pseudo-state-space system to an input-output representation and we develop an algorithm based on the Recursive Least Squares, the Levenberg-marquardt and the Auxiliary Model Principle. The convergence of the identified parameters is studied. The performance of the proposed algorithm are tested by two numerical examples.

关键词： Fractional-order Hammerstein system identification state estimation Levenberg– marquardt algorithm recursive least squares algorithm auxiliary model principle

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Optimal low order model identification of fractional dynamic systems

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期206卷 543-554页

作者： Djamah, T. Mansouri, R. Djennoune, S. Bettayeb, M. Laboratoire de Conception et Conduite des Systèmes de Production University Mouloud Mammeri of Tizi-Ouzou Algeria Department of Electrical and Computer Engineering University of Sharjah United Arab Emirates

This article deals with modeling, simulation, identification and model reduction of non-integer systems in time domain. The fractional order system simulation is based on a fractional integrator operating on a limited spectral range. It allows approximating the fractional system by an integer state-space representation of high dimension. An output error method is used to perform the model parameters identification including the fractional order. Non-integer order systems known to exhibit long memory behavior require high dimensional models to represent them. In this paper, an iterative non-linear programming method is used to perform the approximation reduction and numerical simulations illustrate the efficiency of the reduced model to recover the fractional order system characteristics. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Fractional (non-integer) system System identification Reduced model marquardt algorithm

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