Three-steps modified Levenberg–Marquardt method with a new line search for systems of nonlinear equations

Amini, Keyvan; Rostami, Faramarz

doi:10.1016/j.cam.2015.12.013

Cited by 19 publications

(3 citation statements)

References 15 publications

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“…Levenberg Marquardt (LM) is a widely used optimization algorithm 8 . The convergence speed of LM algorithm is generally higher than the steepest descent method, which simplifies the difficulty of Newton method in calculating Hessian matrix and solves the problem that the approximate Hessian matrix of Gauss Newton method is not full of rank 9,10 .…”

Section: Levenberg-marquardt Algorithmmentioning

confidence: 99%

Design for classification and recognition system of teenager mental health based on LM-BP algorithm

Zhang

Wang

2022

International Conference on Computer Application and Information Security (ICCAIS 2021)

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In order to predict the psychological status of teenagers accurately and quickly and find their psychological problems in time, this paper proposes a BP neural network classification model based on LM algorithm. Compared with BP neural network of steepest descent algorithm, the LM algorithm has better convergence speed and accuracy in the inversion coefficient experiment. In the Chinese text sentiment analysis experiment, the Precision, Recall and F1 values of LM-BP were better than SD-BP. Based on LM-BP model, this paper presents a design scheme of teenagers mental health classification and recognition system. The scheme has good stability, availability and scalability, which lays a technical foundation for the implementation of the system.

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Section: Levenberg-marquardt Algorithmmentioning

confidence: 99%

Design for classification and recognition system of teenager mental health based on LM-BP algorithm

Zhang

Wang

2022

International Conference on Computer Application and Information Security (ICCAIS 2021)

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“…NR method may be faced with challenges of convergence. Newton trust-region method and Levenberg-Marquart (LM) method, which is a type of trust region method, are employed widely to improve the convergence performance of iterative algorithm [14][15][16]. Newton trustregion algorithm is investigated in [17].…”

Section: Introductionmentioning

confidence: 99%

“…} m a b c  ] T , and their dimensions are 3 ×N and 3×(N−NPV) respectively; abc δ is the phase angle column vector of three-phase voltage at both PQ buses and PV buses as well as of phase a at droop buses with dimension of 3 × N−2 × NDroop−1; abc U is the amplitude column vector of three-phase voltage at PQ buses and of phase a at droop buses with dimension of 3×(N−NPV)−2× NDroop. Droop ab P and Droop ab Q are the (2 × NDroop)-dimensional column vectors composed of the active and reactive power output of droop-controlled DGs of phase a and b at droop buses, respectively.Denote the column vector of mismatches of threephase active power and reactive power in(15) as F, i.e. Direct NR algorithm for IMGs…”

mentioning

confidence: 99%

Load flow calculation for droop‐controlled islanded microgrids based on direct Newton–Raphson method with step size optimisation

Zhang

Wu²,

Ding

et al. 2020

IET Generation, Transmission & Distribution

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Load flow calculation for droop-controlled islanded microgrids (IMGs) is different from that of transmission or distribution systems due to the absence of slack bus and the variation of frequency. Meanwhile considering the common three-phase imbalance condition in low-voltage systems, a load flow algorithm based on direct Newton-Raphson (NR) method with step size optimization for both three-phase balanced and unbalanced droop-controlled IMGs is proposed in this paper. First, the steady-state models for balanced and unbalanced droop-controlled IMGs are established based on their operational mechanisms. Then taking frequency as one of the unknowns, the nonlinear load flow equations are solved iteratively by NR method. Generally, iterative load flow algorithms are faced with challenges of convergence performance, especially for unbalanced systems. To tackle this problem, a step-size-optimization scheme is employed to improve the convergence performance for three-phase unbalanced IMGs. In each iteration, a multiplier is deduced from the sum of higherorder terms of Taylor expansion of the load flow equations. Then the step size is optimized by the multiplier which can help smooth the iterative process and obtain the solutions. The proposed method is performed on several balanced and unbalanced IMGs. Numerical results demonstrate the correctness and effectiveness of the proposed algorithm.

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Levenberg-Marquardt Variants in Chrominance-Based Skin Tissue Detection

Kirimtat

Krejcar

Selamat

2019

Bioinformatics and Biomedical Engineering

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Three-steps modified Levenberg–Marquardt method with a new line search for systems of nonlinear equations

Cited by 19 publications

References 15 publications

Design for classification and recognition system of teenager mental health based on LM-BP algorithm

Design for classification and recognition system of teenager mental health based on LM-BP algorithm

Load flow calculation for droop‐controlled islanded microgrids based on direct Newton–Raphson method with step size optimisation

Levenberg-Marquardt Variants in Chrominance-Based Skin Tissue Detection

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