scholarly journals Simultaneous estimation of hydro-dipersive parameters using a new modified levenberg-marquardt algorithm

2019 ◽  
Vol 286 ◽  
pp. 06001
Author(s):  
H. Qanza ◽  
A. Maslouhi ◽  
M. Hachimi ◽  
A. Hmimou
Keyword(s):  
Soil Water ◽  
Least Squares Method ◽  
Numerical Differentiation ◽  
Water Dynamics ◽  
Simultaneous Estimation ◽  
Sensitivity Coefficients ◽  
Marquardt Algorithm ◽  
In Situ Experiments ◽  
Levenberg Marquardt ◽  
Lm Algorithm

Determination of soil hydrodynamic parameters at field scale is of great importance for modeling soil water dynamics and for agricultural water management. The direct estimation of those parameters is time-consuming and afflicted with serious uncertainties. Inverse modeling is known to get efficient technique for solving non-linear problems in hydrology. Levenberg–Marquardt (LM) algorithm is a gradient-based method, which has been widely used for solving inverse soil water flow problems. In the LM algorithm, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if transient states and non-linearities are involved. In this paper, a new approach is proposed for sensitivity analysis using the complex variabledifferentiation method (CVDM) to estimate simultaneously the hydraulic and dispersive properties of unsaturated soil from in-situ experiments. In this approach, the sensitivity coefficients can be determined in a more accurate way than the traditional finite difference method. The results show that the new inverse analysis method in the present work has high accuracy, validity, uniqueness and higher inversion efficiency, compared with the previous least-squares method. The simulated and measured water contents and tracer concentration were generally close. Overall, it was concluded that the CVDM is a promising method to estimate hydro-dispersive parameters in the unsaturated zone.

scholarly journals Processing and Interpretation of UAV Magnetic Data: A Workflow Based on Improved Variational Mode Decomposition and Levenberg-Marquardt Algorithm

Drones ◽  
2022 ◽  
Vol 6 (1) ◽  
pp. 11
Author(s):  
Yaoxin Zheng ◽  
Shiyan Li ◽  
Kang Xing ◽  
Xiaojuan Zhang
Keyword(s):  
Data Processing ◽  
Original Data ◽  
Magnetic Data ◽  
Variational Mode Decomposition ◽  
Euler Deconvolution ◽  
Near Surface ◽  
Mode Decomposition ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Lm Algorithm

Unmanned aerial vehicles (UAVs) have become a research hotspot in the field of magnetic exploration because of their unique advantages, e.g., low cost, high safety, and easy to operate. However, the lack of effective data processing and interpretation method limits their further deployment. In view of this situation, a complete workflow of UAV magnetic data processing and interpretation is proposed in this paper, which can be divided into two steps: (1) the improved variational mode decomposition (VMD) is applied to the original data to improve its signal-to-noise ratio as much as possible, and the decomposition modes number K is determined adaptively according to the mode characteristics; (2) the parameters of target position and magnetic moment are obtained by Euler deconvolution first, and then used as the prior information of the Levenberg–Marquardt (LM) algorithm to further improve its accuracy. Experiments are carried out to verify the effectiveness of the proposed method. Results show that the proposed method can significantly improve the quality of the original data; by combining the Euler deconvolution and LM algorithm, the horizontal positioning error can be reduced from 15.31 cm to 4.05 cm, and the depth estimation error can be reduced from 16.2 cm to 5.4 cm. Moreover, the proposed method can be used not only for the detection and location of near-surface targets, but also for the follow-up work, such as the clearance of targets (e.g., the unexploded ordnance).

scholarly journals Levenberg-marquardt algorithm to identify the fault analysis for industrial applications

2017 ◽  
Vol 7 (1.2) ◽  
pp. 141 ◽  
Author(s):  
P. Bhuvaneswari ◽  
Ramesh G.P
Keyword(s):  
Sensor Network ◽  
Industrial Applications ◽  
Fault Analysis ◽  
Wireless Sensor ◽  
Acoustic Sensor ◽  
Significant Function ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Lm Algorithm ◽  
Flux Sensor

The data are collected and forwarding it to the goal is a significant function of a sensor network. For some applications, it is additionally imperative to admit the fault signal to the collected data. To monitor the industrial environment through a wireless sensor network (WSNs), present a neural network based Levenberg-Marquardt (LM) Algorithm for detecting the fault using the gradient value and mean square error of the signal. The data are collected and presented by the magnetic flux sensor and MEMS acoustic sensor. The simulation model is developed in MATLAB/Simulink.

Comparison of Various Methods for Simultaneous Retrieval of Surface Emissivities and Gas Properties in Gray Participating Media

2006 ◽  
Vol 128 (8) ◽  
pp. 829-837 ◽  
Author(s):  
M. Deiveegan ◽  
C. Balaji ◽  
S. P. Venkateshan
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Heat Fluxes ◽  
Radiative Properties ◽  
Simultaneous Estimation ◽  
Good Precision ◽  
Participating Media ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Artificial Neural

Abstract An inverse radiation analysis for simultaneous estimation of the radiative properties and the surface emissivities for a participating medium in between infinitely long parallel planes, from the knowledge of the measured temperatures and heat fluxes at the boundaries, is presented. The differential discrete ordinate method is employed to solve the radiative transfer equation. The present analysis considers three types of simple scattering phase functions. The inverse problem is solved through minimization of a performance function, which is expressed by the sum of squares of residuals between calculated and observed temperatures and heat fluxes at the boundaries. To check the performance and accuracy in retrieval, a comparison is presented between four retrieval methods, viz. Levenberg-Marquardt algorithm, genetic algorithm, artificial neural network, and the Bayesian algorithm. The results of the present analyses indicate that good precision in retrieval could be achieved by using only temperatures and heat fluxes at the boundaries. The study shows that the radiative properties of medium and surface emissivities can be retrieved even with noisy data using Bayesian retrieval algorithm and artificial neural network. Also, the results demonstrate that genetic algorithms are not efficient but are quite robust. Additionally, it is observed that an increase in the error in measurements significantly deteriorates the retrieval using the Levenberg-Marquardt algorithm.

scholarly journals Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2176
Author(s):  
Zhiqi Yan ◽  
Shisheng Zhong ◽  
Lin Lin ◽  
Zhiquan Cui
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Frequency Noise ◽  
Optimization Strategy ◽  
Engineering Data ◽  
Marquardt Algorithm ◽  
Highly Nonlinear ◽  
Rectified Linear Unit ◽  
Levenberg Marquardt ◽  
Lm Algorithm

Engineering data are often highly nonlinear and contain high-frequency noise, so the Levenberg–Marquardt (LM) algorithm may not converge when a neural network optimized by the algorithm is trained with engineering data. In this work, we analyzed the reasons for the LM neural network’s poor convergence commonly associated with the LM algorithm. Specifically, the effects of different activation functions such as Sigmoid, Tanh, Rectified Linear Unit (RELU) and Parametric Rectified Linear Unit (PRLU) were evaluated on the general performance of LM neural networks, and special values of LM neural network parameters were found that could make the LM algorithm converge poorly. We proposed an adaptive LM (AdaLM) algorithm to solve the problem of the LM algorithm. The algorithm coordinates the descent direction and the descent step by the iteration number, which can prevent falling into the local minimum value and avoid the influence of the parameter state of LM neural networks. We compared the AdaLM algorithm with the traditional LM algorithm and its variants in terms of accuracy and speed in the context of testing common datasets and aero-engine data, and the results verified the effectiveness of the AdaLM algorithm.

scholarly journals Modification of Levenberg-Marquardt Algorithm for Solve Two Dimension Partial Differential Equation

2018 ◽  
Vol 26 (7) ◽  
pp. 107-117
Author(s):  
Khalid Mindeel M. Al-Abrahemee ◽  
Rana T. Shwayaa
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Partial Differential ◽  
Two Dimension ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
In The Beginning ◽  
Lm Algorithm

In this paper we presented a new way based on neural network has been developed for solutione of two dimension  partial differential equations . A modified neural network use to over passing the Disadvantages of LM algorithm, in the beginning we suggest signaler value decompositions of Jacobin matrix (J) and inverse of Jacobin matrix( J-1), if a matrix rectangular or singular  Secondly, we suggest new calculation of μk , that ismk=|| E (w)||2    look the nonlinear execution equations E(w) = 0 has not empty solution W* and we refer   to the second norm in all cases ,whereE(w):  is continuously differentiable and E(x) is Lipeschitz  continuous, that is=|| E(w 2)- E(w 1)||£ L|| w  2- w  1|| ,where L  is Lipeschitz  constant.

scholarly journals Improving Levenberg-Marquardt Algorithm Inversion Result Using Singular Value Decomposition

2016 ◽  
Vol 5 (2) ◽  
pp. 20
Author(s):  
Widodo Widodo ◽  
Durra Handri Saputera
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Parameter Analysis ◽  
Model Parameters ◽  
Inversion Result ◽  
One Dimensional ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Value Decomposition ◽  
Lm Algorithm

Inversion is a process to determine model parameters from data. In geophysics this process is very important because subsurface image is obtained from this process. There are many inversion algorithms that have been introduced and applied in geophysics problems; one of them is Levenberg-Marquardt (LM) algorithm. In this paper we will present one of LM algorithm application in one-dimensional magnetotelluric (MT) case. The LM algorithm used in this study is improved version of LM algorithm using singular value decomposition (SVD). The result from this algorithm is then compared with the algorithm without SVD in order to understand how much it has been improved. To simplify the comparison, simple synthetic model is used in this study. From this study, the new algorithm can improve the result of the original LM algorithm. In addition, SVD is allowing more parameter analysis to be done in its process. The algorithm created from this study is then used in our modeling program, called MAT1DMT.

scholarly journals Fast Cylindrical Fitting Method Using Point Cloud’s Normals Estimation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yunlong Wu ◽  
Qing Zhang ◽  
Shuxuan Zhang
Keyword(s):  
Coordinate Transformation ◽  
Point Cloud ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Essential Step ◽  
Initial Values ◽  
Fitting Method ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

Cylindrical fitting is an essential step in Large Process Pipeline’s measurement process, and precision of initial values of cylindrical fitting is a key element in getting a correct fitting result. In order to get well initial values, covariance matrixes of all points in cylinder’s three-dimensional laser scanning point cloud should be firstly established to estimate normals of all points, and then cylinder’s axis vector can be calculated by using least squares method. Secondly, remaining parameters’ initial values of the cylinder can be got by coordinate transformation. Finally, Levenberg-Marquardt algorithm is used in iterative optimization process to get fitting result by using the above values as initial values. Experiments demonstrate that this method can get precise initial values of cylindrical fitting and improve the accuracy and speed of cylindrical fitting.

scholarly journals Local Levenberg-Marquardt Algorithm for Learning Feedforwad Neural Networks

2020 ◽  
Vol 10 (4) ◽  
pp. 299-316 ◽  
Author(s):  
Jarosław Bilski ◽  
Bartosz Kowalczyk ◽  
Alina Marchlewska ◽  
Jacek M. Zurada
Keyword(s):  
Neural Networks ◽  
Computational Complexity ◽  
Function Approximation ◽  
Classification Problems ◽  
Local Computation ◽  
Method Performance ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Local Modification ◽  
Lm Algorithm

AbstractThis paper presents a local modification of the Levenberg-Marquardt algorithm (LM). First, the mathematical basics of the classic LM method are shown. The classic LM algorithm is very efficient for learning small neural networks. For bigger neural networks, whose computational complexity grows significantly, it makes this method practically inefficient. In order to overcome this limitation, local modification of the LM is introduced in this paper. The main goal of this paper is to develop a more complexity efficient modification of the LM method by using a local computation. The introduced modification has been tested on the following benchmarks: the function approximation and classification problems. The obtained results have been compared to the classic LM method performance. The paper shows that the local modification of the LM method significantly improves the algorithm’s performance for bigger networks. Several possible proposals for future works are suggested.

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