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self-adaptive system state optimization based on nonlinear affine transformation for renewable energy volatility

RENEWABLE ENERGY 2024年 230卷

作者： Zhang, Zhaoyi Han, Zixi Hu, Hao Fan, Youping Fan, Jianbin Shu, Yinbiao Wuhan Univ Sch Elect Engn & Automat Wuhan 430072 Peoples R China Wuhan Univ Inst Next Generat Power Syst & Int Stand Wuhan 430072 Peoples R China

The short-term power variations of renewable energy sources result in system state fluctuations and deviations from the scheduled operating point. Tracking short-term power variations and maintaining the system's optimality is challenging for traditional optimization methods due to their highly time-consuming nature. This paper proposes a short-timescale self -adaptive optimization strategy based on the nonlinear affine transformation to deal with this problem. Firstly, the multi -period optimization model is established and solved by considering static power -frequency characteristics to obtain an optimal operating point on a longer temporal scale, with the state security margins reserved using chance constraint programming. Next, analogously with the Taylor series, the nonlinear relationship between the system state variable and short-term power fluctuations is revealed through an analytic expression of the nonlinear affine transformation. Then, a self -adaptive optimization algorithm based on the nonlinear affine transformation is proposed to achieve frequency and voltage optimizations on a shorter temporal scale. With less communication, self -adaptive optimization is implemented at the local bus level to achieve more optimal states for short-term renewable power variations rapidly. Finally, simulations demonstrate that the proposed optimization strategy can effectively enhance frequency and voltage qualities, and decrease objective function, thereby improving the operation safety and economy.

关键词： self-adaptive algorithm Renewable energy sources Short-term power fluctuations Nonlinear affine transformation Energy storage devices Taylor series

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Reckoning solution of split common fixed point problems by using inertial self-adaptive algorithms

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2019年第4期113卷 3101-3114页

作者： Suparatulatorn, Raweerote Suantai, Suthep Phudolsitthiphat, Narawadee Chiang Mai Univ Fac Sci Dept Math Res Ctr Math & Appl Math Chiang Mai 50200 Thailand

In this paper, we construct a novel algorithm for the split common fixed point problem for two demicontractive operators in Hilbert spaces. By using inertial self-adaptive algorithms, we obtain strong convergence results for finding a solution of the split common fixed point problems. Applications to solving the split minimization problem and the split feasibility problem are included. Our results extend and generalizemany previously known results in this research area. Moreover, numerical experiments are supplied to demonstrate the convergence behavior and efficiency of the proposed algorithm.

关键词： Split common fixed point problem Demicontractive operator self-adaptive algorithm Inertial algorithm

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Inertial accelerated algorithms for the split common fixed-point problem of directed operators

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OPTIMIZATION 2021年第5-6期70卷 1375-1407页

作者： Zhao, Jing Zhao, Ning-ning Hou, Dingfang Civil Aviat Univ China Coll Sci Tianjin Peoples R China Civil Aviat Univ China Coll Air Traff Management Tianjin Peoples R China

In this paper, we introduce two inertial accelerated algorithms for solving the split common fixed-point problem of directed operators in real Hilbert space. The proposed iterative algorithms combine the primal-dual method and the inertial method with the self-adaptive stepsizes such that the implementation of our algorithms does not need any prior information about bounded linear operator norms. Under suitable conditions, the weak and strong convergence results of the algorithms are obtained. Numerical results which involve image restoration problems are reported to show the effectiveness of the proposed algorithms.

关键词： Split common fixed-point problem directed operator inertial technique self-adaptive algorithm weak convergence

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Inertial relaxedCQalgorithms for solving a split feasibility problem in Hilbert spaces

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NUMERICAL algorithmS 2021年第3期87卷 1075-1095页

作者： Sahu, D. R. Cho, Y. J. Dong, Q. L. Kashyap, M. R. Li, X. H. Banaras Hindu Univ Inst Sci Dept Math Varanasi 221005 Uttar Pradesh India Gyeongsang Natl Univ Dept Math Educ Jinju 52828 South Korea Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Sichuan Peoples R China Key Lab Adv Signal Proc Tianjin 300300 Peoples R China Coll Sci Tianjin 300300 Peoples R China Civil Aviat Univ China Tianjin 300300 Peoples R China

The split feasibility problem is to find a pointx*with the property thatx*is an element of CandAx*is an element of Q, whereCandQare nonempty closed convex subsets of real Hilbert spacesXandY, respectively, andAis a bounded linear operator fromXtoY. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxedCQalgorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposedCQalgorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.

关键词： Split feasibility problem CQ algorithm Inertial technique self-adaptive algorithm Weak convergence

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Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期73卷 637-657页

作者： Pham Ky Anh Trinh Ngoc Hai Vietnam Natl Univ Dept Math 334 Nguyen Trai Hanoi Vietnam Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

In this paper, we introduce two self-adaptive algorithms for solving a class of non-Lipschitz equilibrium problems. These algorithms are very simple in the sense that at each step, they require only one projection onto a feasible set. Their convergence can be established under quite mild assumptions. More precisely, the weak (strong) convergence of the first algorithm is proved under the pseudo-paramonotonicity (strong pseudomonotonicity) conditions, respectively. Especially, the convexity in the second argument of the involving bifunction is not required. In the second algorithm, the weak convergence is established under the pseudomonotonicity. Moreover, it is proved that under some additional conditions, the solvability of the equilibrium problem is equivalent to the boundedness of the sequences generated by the proposed algorithms. Some applications to the optimization problems and variational inequality problems as well as to transport equilibrium problems are also considered.

关键词： Equilibrium problem Variational inequality Fixed point problem Solution existence Non-convex optimization self-adaptive algorithm

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A novel rotated sigmoid weight function for higher performance in heterogeneous deformation measurement with digital image correlation

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OPTICS AND LASERS IN ENGINEERING 2022年 159卷

作者： Ye, Xiaosen Zhao, Jiaqing Tsinghua Univ Collaborat Innovat Ctr Adv Nucl Energy Technol Inst Nucl & New Energy Technol Key Lab Adv Reactor Engn & SafetyMinist Educ Beijing 100084 Peoples R China

Conventional digital image correlation (C-DIC) combined with a rotated Gaussian weight (RGW) function for subset has demonstrated attractive ability in resolving heterogeneous deformation parameters. To further improve the performance, the selection of an optimum weight function becomes the key issue. In this paper, a novel rotated sigmoid weight (RSW) function is proposed. RSW function aims to get a more uniform weight distribution near the subset center, and to realize the continuous change of the equivalent subset size as well. The performance of the RSW function is compared with the Gaussian weight (GW) function, RGW function, the rotated inverse distance weight (RIDW) function and the inverse distance square weight (RIDSW) function through Star 5 image set from the DIC challenge 2.0 and the simulated image set. A total of six methods with different weight functions and rotated weights are systematically compared. The experiment results clearly show that DIC combined with RSW function (i.e. RSW-DIC) has the best spatial resolution without sacrificing much measurement resolution. The spatial resolution of RSW-DIC is only about half of the other methods for both first- and second-order shape functions when a big initial subset size is adopted.

关键词： Digital image correlation Heterogeneous deformation measurement self-adaptive algorithm

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self-adaptive algorithms for the split problem of the demicontractive operators

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OPTIMIZATION 2018年第9期67卷 1309-1319页

作者： Yao, Yonghong Liou, Yeong-Cheng Postolache, Mihai Tianjin Polytech Univ Dept Math Tianjin Peoples R China Kaohsiung Med Univ Dept Healthcare Adm & Med Informat Kaohsiung Taiwan Kaohsiung Med Univ Res Ctr Nonlinear Anal & Optimizat Kaohsiung Taiwan Kaohsiung Med Univ Hosp Dept Med Res Kaohsiung Taiwan China Med Univ Dept Neural Comp Taichung Taiwan Univ Politehn Bucuresti Dept Math & Informat Bucharest Romania

self-adaptive algorithms are presented for solving the split common fixed point problem of demicontractive operators in Hilbert spaces. Weak and strong convergence theorems are given under some mild assumptions.

关键词： Split common fixed point demicontractive operator self-adaptive algorithm

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A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps in winter conditions

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APPLIED MATHEMATICAL MODELLING 2020年 83卷 284-300页

作者： Tang, Jinchen Herman, Cila Gong, Guangcai Chinese Acad Sci Inst Engn Thermophys Beijing 100190 Peoples R China Johns Hopkins Univ Dept Mech Engn Baltimore MD 21218 USA Hunan Univ Civil Engn Coll Changsha 410082 Hunan Peoples R China

As frost accumulates on the heat exchanger surface with time, system operating performance will be dramatically degraded, and limit its use in climates susceptible to frost formation. A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps (ASHP) is introduced in this paper. The control strategy relies on a new thermodynamic model, which involves a Dimensionless Artificial Neural Network (DANN) correlation model describing frost accumulation for ASHP on the air-side of the fin-and-tube heat exchanger. The dimensionless parameters of this DANN model, including the ambient conditions, 6 commonly used refrigerants, and the geometric parameters of the heat exchanger, are considered in the model. To enhance the reliability of DANN, we develop a self-adaptive algorithm, including determining the optimal transfer algorithm and selecting the number of neurons in the hidden layer, for the DANN model. Results show a limited relative error (7.55%) between calculated values and experimental data, which help researchers and manufacturers analyze the complicated frosting process and design the new ASHPs more reasonably in different regions with different ambient conditions. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Dimensionless model Air source heat pump Frost accumulation Different refrigerants Artificial neural networks self-adaptive algorithm

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An algorithm for the split feasible problem and image restoration

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2020年第1期115卷 1-18页

作者： Suparatulatorn, Raweerote Charoensawan, Phakdi Poochinapan, Kanyuta Dangskul, Supreedee Chiang Mai Univ Adv Res Ctr Computat Simulat Fac Sci Chiang Mai 50200 Thailand Chiang Mai Univ Dept Math Fac Sci Chiang Mai 50200 Thailand CHE Ctr Excellence Math Si Ayutthaya Rd Bangkok 10400 Thailand

This paper proposes an accelerated algorithm for the split common fixed point problem, based on viscosity approximation methods and inertial effects. The main result will be applied to image restoration problems. This algorithm is constructed in such a way that its step sizes and the norm of a given linear operator are not related. Under some conditions, the strong convergence of the algorithm is obtained. Numerical investigations are carried out in order to illustrate high-performance of the present work, mainly using processing duration and the signal-to-noise ratio. It is also shown that this proposed algorithm is more efficient and effective than the published algorithm by Yao et al.

关键词： Split common fixed point problem Demicontractive operator self-adaptive algorithm Inertial algorithm Image restoration problem

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Convergence rate of a new projected-type algorithm solving non-Lipschitz equilibrium problems

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COMPUTATIONAL & APPLIED MATHEMATICS 2020年第2期39卷 52-52页

作者： Hai Trinh Ngoc Hanoi Univ Sci & Technol Sch Appl Math & Informat 1st Dai Co Viet St Hanoi Vietnam

In this paper, we introduce a new step size strategy for projection-type algorithms for solving strongly pseudomonotone equilibrium problems in a Hilbert space. In contrast to the work by Anh et al. (Numer algorithms. 10.1007/s11075-018-0578-z, 2017) and by Santos et al. (Comput Appl Math 30:91-107, 2011), our methods do not require the step sizes being square summable. Moreover, at each step of the proposed algorithms, instead of solving a constrained problem, we only have to solve an unconstrained problem and compute a projection onto the feasible set or its intersection with a closed sphere. The strong convergence of the proposed algorithms is proven without any Lipschitz-type condition. Also, we evaluate the convergence rate of these algorithms. Using cutting hyperplanes, we refine the feasible set at the beginning of our algorithms. Thanks to this, we can apply the new algorithms to the equilibrium problems with non-closed and non-convex feasible set. Some numerical experiments and comparisons confirm efficiency of the proposed modification.

关键词： Equilibrium problem self-adaptive algorithm Shrinking feasible set Strong pseudomonotonicity

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