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Modeling of multistage nonlinear Dual Mass Flywheel torsional damper based on smoothing function fitting

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2021年第1期235卷 32-42页

作者： Long, Chen Wen-ku, Shi Song, Li Zhi-yong, Chen Yuan-bin, Yu Jilin Univ State Key Lab Automot Simulat & Control 5988 Renmin St Changchun 130022 Jilin Peoples R China

The smoothing function is used to solve the problem of low simulation efficiency of multi-stage stiffness Dual Mass Flywheel (DMF) model, and the influence of different smoothing functions and fitting factor beta on the fitting effect is studied. Firstly, based on the analysis of the working principle of multi-stage stiffness DMF, a mathematical model of DMF considering multi-stage stiffness and damping nonlinearity is established, and the accuracy of the model is verified by bench test. Then, tanh function, arctangent function, and sigmoid function are used to smooth the segment points in the DMF model, which solves the problem of inefficiency and not easy to converge in simulation. Finally, a 3-DOF model of the transmission system with DMF is established to simulate and analyze the smooth effect of the smoothing function and the performance difference between different smoothing functions. The results show that the smoothing function can effectively improve the stability of the simulation model. By comparing the three smoothing functions, it can be seen that the sigmoid function has the most obvious effect, which can shorten the simulation time by 52%.

关键词： Multi-stage stiffness Dual Mass Flywheel torsion characteristic smoothing function

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New smoothing function for solving absolute value equations

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ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2023年第12期16卷

作者： Chalekh, Randa Djeffal, El Amir Univ Batna 2 Math Dept LEDPA Lab Batna 05000 Algeria

In this paper, we use a smoothing-type algorithm in this paper to solve the AVE, which stands for the absolute value equation Ax-|x|=b , where A is an arbitrary nxn real matrix and b is an element of R-n. We reformulate AVE as a system of smooth equations and propose two new smoothing functions. We prove that the algorithm is well-defined when the singular value of A exceeds one, and under the same assumption, the algorithm is convergent. We show the algorithm's effectiveness with these two functions and compare it with some previously known functions.

关键词： Absolute value equations smoothing Newton algorithm smoothing function convergence

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Phase Retrieval Algorithm via Nonconvex Minimization Using a smoothing function

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第17期66卷 4574-4584页

作者： Pinilla, Samuel Bacca, Jorge Arguello, Henry Univ Ind Santander Dept Elect & Comp Engn Bucaramanga 680002 Colombia Univ Ind Santander Dept Comp Sci Bucaramanga 680002 Colombia

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smoothing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms.

关键词： Non-convex problem non-smooth function phase retrieval smoothing function

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Fuzzy Controller used smoothing function for Depth Control of Autonomous Underwater Vehicle

Fuzzy Controller used Smoothing Function for Depth Control o...

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OCEANS Conference

作者： Wang, Yue Shen, Yue Wang, Kaihong Sha, Qixin He, Bo Yan, Tianhong Ocean Univ China Sch Informat Sci & Engn Qingdao Peoples R China China Jiliang Univ Dept Mech & Elect Engn Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9781467397247

Autonomous Underwater Vehicle (AUV) is a typical system which is characterized by nonlinearity, uncertainty of system parameters, and it is also affected by many external disturbances. Therefore, it is difficult to achieve the accurate AUV motion control, which includes depth control, heading control and so on. In order to improve the stability and robustness of depth control system of AUV, this paper researches the model of AUV's motion, analyzes the characteristics of the main existing methods for AUV depth control, including PID, variable structure control (VSC) and fuzzy logic control (FLC). Then, a new method of fuzzy controller used smoothing function (SFFC) for depth control of AUV is proposed based on VSC and fuzzy logic. Finally, simulation and comparison experiments based on dynamic model of AUV are carried out to verify the validity of this method. The results show that the SFFC has better stability and robustness for AUV's depth control system than VSC and PID control.

关键词： fuzzy logic control smoothing function dynamic model of AUV depth control

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smoothing functions and algorithm for nonsymmetric circular cone complementarity problems

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APPLICATIONS OF MATHEMATICS 2022年第2期67卷 209-231页

作者： Tang, Jingyong Chen, Yuefen Xinyang Normal Univ Coll Math & Stat Xinyang 464000 Peoples R China

There has been much interest in studying symmetric cone complementarity problems. In this paper, we study the circular cone complementarity problem (denoted by CCCP) which is a type of nonsymmetric cone complementarity problem. We first construct two smoothing functions for the CCCP and show that they are all coercive and strong semismooth. Then we propose a smoothing algorithm to solve the CCCP. The proposed algorithm generates an infinite sequence such that the value of the merit function converges to zero. Moreover, we show that the iteration sequence must be bounded if the solution set of the CCCP is nonempty and bounded. At last, we prove that the proposed algorithm has local superlinear or quadratical convergence under some assumptions which are much weaker than Jacobian nonsingularity assumption. Some numerical results are reported which demonstrate that our algorithm is very effective for solving CCCPs.

关键词： circular cone complementarity problem smoothing function smoothing algorithm superlinear quadratical convergence

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A smoothing function Approach to Joint Chance-Constrained Programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第1期163卷 181-199页

作者： Shan, Feng Zhang, Liwei Xiao, Xiantao Shenyang Univ Aeronaut & Astronaut Inst Operat Res Fac Sci Shenyang Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China

In this article, we consider a DC (difference of two convex functions) function approach for solving joint chance-constrained programs (JCCP), which was first established by Hong et al. (Oper Res 59:617-630, 2011). They used a DC function to approximate the probability function and constructed a sequential convex approximation method to solve the approximation problem. However, the DC function they used was nondifferentiable. To alleviate this difficulty, we propose a class of smoothing functions to approximate the joint chance-constraint function, based on which smooth optimization problems are constructed to approximate JCCP. We show that the solutions of a sequence of smoothing approximations converge to a Karush-Kuhn-Tucker point of JCCP under a certain asymptotic regime. To implement the proposed method, four examples in the class of smoothing functions are explored. Moreover, the numerical experiments show that our method is comparable and effective.

关键词： Joint chance-constrained programs smoothing function Sequential convex approximation method DC function

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An augmented Lagrangian multiplier method based on a CHKS smoothing function for solving nonlinear bilevel programming problems

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KNOWLEDGE-BASED SYSTEMS 2014年 55卷 9-14页

作者： Jiang, Yan Li, Xuyong Huang, Chongchao Wu, Xianing Chinese Acad Sci State Key Lab Urban & Reg Ecol Res Ctr Ecoenvironm Sci Beijing 100085 Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Sinohydro Resources Ltd Beijing 100048 Peoples R China

Bilevel programming techniques deal with decision processes involving two decision makers with a hierarchical structure. In this paper, an augmented Lagrangian multiplier method is proposed to solve nonlinear bilevel programming (NBLP) problems. An NBLP problem is first transformed into a single level problem with complementary constraints by replacing the lower level problem with its Karush-Kuhn-Tucker optimality condition, which is sequentially smoothed by a Chen-Harker-Kanzow-Smale (CHKS) smoothing function. An augmented Lagrangian multiplier method is then applied to solve the smoothed nonlinear program to obtain an approximate optimal solution of the NBLP problem. The asymptotic properties of the augmented Lagrangian multiplier method are analyzed and the condition for solution optimality is derived. Numerical results showing viability of the approach are reported. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Nonlinear bilevel programming Karush-Kuhn-Tucker condition Complementary constraints smoothing function Augmented Lagrangian multiplier method

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Constructive Method for Appropriate Membership function Integrating Fuzzy Entropy with smoothing function into Interval Estimation 7

Constructive Method for Appropriate Membership Function Inte...

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Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS) and 15th International Symposium on Advanced Intelligent Systems (ISIS)

作者： Hasuike, Takashi Katagiri, Hideki Tsubaki, Hiroe Osaka Univ Grad Sch Informat Sci & Technol 2-1 Yamadaoka Suita Osaka 5650871 Japan Hiroshima Univ Grad Sch Engn Higashihiroshima Hiroshima 7398527 Japan Inst Stat Math Dept Data Sci Tachikawa Tokyo 1908562 Japan

ISBN: (纸本)9781479959556

This paper develops a constructing approach of a membership function to integrate the fuzzy Shannon entropy with a smoothing function into intervals set by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in decision making. Therefore, the main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the problem efficiently using previous constructing approaches. In this paper, performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each membership value is developed.

关键词： constructive method for membership function fuzzy entropy smoothing function mathematical programming

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Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第3期202卷 1421-1445页

作者： Guo, Lei Li, Gaoxi East China Univ Sci & Technol Sch Business Shanghai 200237 Peoples R China Chongqing Technol & Business Univ Sch Math & Stat Chongqing 400067 Peoples R China

We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz MPEC is highly challenging since the standard constraint qualifications fail due to the existence of equilibrium constraints and the subdifferential of the objective function is unbounded due to the existence of the non-Lipschitz function. On the one hand, for tackling the non-Lipschitzness of the objective function, we introduce a novel class of locally Lipschitz approximation functions that consolidate and unify a diverse range of existing smoothing techniques for the non-Lipschitz function. On the other hand, we use the Kanzow and Schwartz regularization scheme to approximate the equilibrium constraints since this regularization can preserve certain perpendicular structure as in equilibrium constraints, which can induce better convergence results. Then an approximation method is proposed for solving the non-Lipschitz MPEC and its convergence is established under weak conditions. In contrast with existing results, the proposed method can converge to a better stationary point under weaker qualification conditions. Finally, a computational study on the sparse solutions of linear complementarity problems is presented. The numerical results demonstrate the effectiveness of the proposed method.

关键词： Mathematical program with equilibrium constraints Nonconvex optimization Non-Lipschitz continuity Sparsity-inducing penalty smoothing function Regularization method

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A NON-MONOTONE smoothing NEWTON ALGORITHM FOR SOLVING THE SYSTEM OF GENERALIZED ABSOLUTE VALUE EQUATIONS

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Journal of Computational Mathematics 2025年第2期43卷 438-460页

作者： Cairong Chen Dongmei Yu Deren Han Changfeng Ma School of Mathematics and Statistics Key Laboratory of Analytical Mathematics and Applications(Ministry of Education)Fujian Provincial Key Laboratory of Statistics and Artificial IntelligenceFujian Normal UniversityFuzhou 350117P.R.China Institute for Optimization and Decision Analytics College of ScienceLiaoning Technical UniversityFuxin 123000P.R.China LMIB of the Ministry of Education School of Mathematical SciencesBeihang UniversityBeijing 100191P.R.China

The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization *** this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the *** show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the *** results are given to demonstrate the viability and efficiency of the approach.

关键词： Generalized absolute value equations smoothing function smoothing Newton algorithm Non-monotone line search Global and local quadratic convergence

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