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Gauss-Newton Runge-Kutta integration for efficient discretization of optimal control problems with long horizons and least-squares costs

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EUROPEAN JOURNAL OF CONTROL 2024年 80卷

作者： Frey, Jonathan Baumgaertner, Katrin Diehl, Moritz Univ Freiburg Dept Microsyst Engn IMTEK Freiburg Germany Univ Freiburg Dept Math Freiburg Germany

This work proposes an efficient treatment of continuous-time optimal control problems with long horizons and nonlinear least-squares costs. In particular, we present the Gauss-Newton Runge-Kutta (GNRK) integrator which provides a high-order cost integration. Crucially, the Hessian of the cost terms required within SQP-type algorithm is approximated with a Gauss-Newton Hessian. Moreover, L2 penalty formulations constraints are shown to be particularly effective for optimization with GNRK. An efficient implementation of GNRK is provided in the open-source software framework acados. We demonstrate the effectiveness the proposed approach and its implementation on an illustrative example showing a reduction of relative suboptimality by a factor greater than 10 while increasing the runtime by only 10%.

关键词： Optimal control optimization algorithms optimization

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Automatic variogram model fitting of a variogram map based on the Fourier integral method

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COMPUTERS & GEOSCIENCES 2021年 156卷 104891-104891页

作者： de Carvalho, Paulo Roberto Moura da Costa, Joao Felipe Coimbra Leite Fed Univ Rio Grande do Sul UFRGS Av Bento Goncalves 9500Bloco 4Predio 75 BR-91501970 Porto Alegre RS Brazil Petr Brasileiro SA Av Horacio de Macedo 9503 AndarEscritorio 1 BR-21941915 Rio De Janeiro RJ Brazil

One of the cornerstones of geostatistics is the variogram. Fitting a variogram model to observed data is certainly one of the routine tasks in daily geostatistics practice. The central role of the variogram and the difficulty of performing variogram modeling manually call for an automatic, or at least a computer-assisted, method. Fitting a parametric curve to observational points in an XY chart is far from new and the GSLib software package has included a module (called VARFIT) to perform automatic variogram fitting in 1D since its debut many years ago. Nevertheless, extending its objective function to fitting to variogram map (2D) resulted in a method with poor performance. Hence, this work proposes a computational method to fit variogram models to variogram maps with a different objective function based on the principles of the Fourier Integral Method (FIM). A map is synthesized from the theoretical variogram model using the principles of FIM. The metric of the objective function is the sum of squares of differences between each pixel value of the synthetic map and the input map. The genetic algorithm uses this metric to find the variogram parameters of a model with good fitness. Since the genetic algorithm has a stochastic component, the best fit is not certain. Hence, several runs with different random number generator seeds are performed. The parameters of all fitted models are collected and cluster analysis in parameter space is done with the DBSCAN algorithm. The centers of the clusters are the parameters of the sought variogram model. Open-source software was written and made available, in which the proposed objective function was tested alongside the 2D version of the one in VARFIT. Results showed better effectiveness of the proposed method in fitting variogram models for the variogram map case.

关键词： Geostatistics Automatic variogram modeling Fourier integral method optimization algorithms Clustering algorithms

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Q-learning embedded sine cosine algorithm (QLESCA)

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期193卷 116417-116417页

作者： Hamad, Qusay Shihab Samma, Hussein Suandi, Shahrel Azmin Mohamad-Saleh, Junita Univ Sains Malaysia Sch Elect & Elect Engn Engn Campus Nibong Tebal 14300 Penang Malaysia Univ Teknol Malaysia Fac Engn Sch Comp Soft Comp Res Grp Johor Baharu 81310 Johor Malaysia Univ Informat Technol & Commun UOITC Baghdad Iraq

Sine Cosine Algorithm (SCA) was recognized as a lightweight, efficient, and has a clear math principal optimizer. However, SCA still suffers from a set of problems such as stagnation at local optima, a slow convergence curve, and a lack of efficient balancing between exploration and exploitation search modes. To mitigate these limitations and improve SCA performance, this study introduces a new version of SCA called QLESCA that smartly controls SCA parameters through an embedded Q-learning algorithm at run time. Each QLESCA agent evolves independently, and it has its own Q-table. The Q-table contains nine different states computed based on population density and distance from the micro population leader. As such, nine different actions are generated by Q-table to control QLESCA parameters, namely r(1) and r(3). These QLESCA parameters are responsible for adaptive switching from exploration/exploitation and vice versa. For each Q-table action, a reward value is given to a well-performing agent and a penalty to a non-performing agent. To verify the proposed algorithm's performance, QLESCA was evaluated with 23 continuous benchmarks, 20 large scale benchmark optimization functions, and three engineering design problems. In addition, the conducted analysis was compared with various SCA variant algorithms and other state-of-the-art swarm-based optimization methods. The numerical results demonstrate that the QLESCA was superior in terms of achieved fitness value. Statistical results confirm that QLESCA significantly outperforms other optimization algorithms. Additionally, the convergence curve outcomes show that the proposed QLESCA optimization obtains fast convergence against other conducted algorithms.

关键词： Since cosine optimizer Swarm intelligence Q-learning algorithm optimization algorithms Metaheuristic algorithm Large-scale problems

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Freeform optics design advances lighting and illumination

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LASER FOCUS WORLD 2011年第3期47卷 36-38页

作者： Fournier, Florian Cassarly, William Synopsys Opt Solut Grp Illuminat Engn Pasadena CA 91107 USA

Freef orm design solutions The flux mapping method consists of finding a correspondence (map) between the source and the desired target light distribution.1 The flux distributions of the point source and the target are both divided into bins containing equal amounts of energy. [...] what matters is the size of the source relative to the size of the optics and target.

关键词： Methods optimization algorithms Computer aided design--CAD Design engineering Light emitting diodes

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Modeling and optimal operation of hybrid wave energy and PV system feeding supercharging stations based on golden jackal optimal control strategy

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ENERGY 2023年第PartD期263卷

作者： Mahdy, Ahmed Hasanien, Hany M. Turky, Rania A. Aleem, Shady H. E. Abdel Ain Shams Univ Fac Engn Elect Power & Machines Dept Cairo 11517 Egypt Future Univ Egypt Fac Engn & Technol Elect Engn Dept Cairo 11835 Egypt Sci Valley Acad Valley High Inst Engn & Technol Dept Elect Engn Qalyubia 44971 Egypt

This paper provides a novel application for the Archimedes wave swing (AWS) device that converts the sea waves into electrical energy using a linear permanent magnet synchronous generator (LPMSG), which is connected to a rectifier that extracts the most significant energy from sea waves and reduces the stator losses. The generator's power combined with a photovoltaic (PV) system provides a total of 250 kW, sufficient for feeding a V3 Tesla Supercharging system, which is currently the latest and most advanced electric vehicle (EV) charging technology. The hybrid system is connected to a DC link, its voltage is stabilized using a supercapacitor energy storage system, and the output is provided to a buck converter that reduces the voltage for the Tesla Supercharger. The control system comprises seven proportional-integral (PI) controllers with four anti-wind back-calculation co-efficients to improve transient stability. The PI gains are optimized using the Golden Jackal optimization Al-gorithm (GJOA), and the system stability is evaluated by applying different disturbances like a sudden variation in the DC load, temporary DC short circuit, and connection of the EV in various modes such as a grid to vehicle and vehicle to grid modes. The results obtained by the GJOA are compared with the Particle Swarm optimization and the hybrid Augmented Grey Wolf Optimizer and Cuckoo Search algorithms. Finally, hybrid renewable en-ergy systems can efficiently be employed in EV supercharging stations as validated with the strategy proposed in this work.

关键词： Archimedes wave swing Electric vehicles Hybrid renewable energy systems optimization algorithms Photovoltaic system Wave power application

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An Agile Approach for Adopting Sustainable Energy Solutions with Advanced Computational Techniques

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ENERGIES 2024年第13期17卷 3150页

作者： Konneh, David Abdul Howlader, Harun Or Rashid Elkholy, M. H. Senjyu, Tomonobu Univ Ryukyus Dept Elect & Elect Engn Nishihara Okinawa 9030213 Japan Univ Hawaii Hawaii Nat Energy Inst Grid START Res Corp Honolulu HI 96822 USA

In the face of the burgeoning electricity demands and the imperative for sustainable development amidst rapid industrialization, this study introduces a dynamic and adaptable framework suitable for policymakers and renewable energy experts working on integrating and optimizing renewable energy solutions. While using a case study representative model for Sub-Saharan Africa (SSA) to demonstrate the challenges and opportunities present in introducing optimization methods to bridge power supply deficits and the scalability of the model to other regions, this study presents an agile multi-criteria decision tool that pivots on four key development phases, advancing established methodologies and pioneering refined computational techniques, to select optimal configurations from a set of Policy Decision-Making Metrics (PDM-DPS). Central to this investigation lies a rigorous comparative analysis of variants of three advanced algorithmic approaches: Swarm-Based Multi-objective Particle Swarm optimization (MOPSO), Decomposition-Based Multi-objective Evolutionary Algorithm (MOEA/D), and Evolutionary-Based Strength Pareto Evolutionary Algorithm (SPEA2). These are applied to a grid-connected hybrid system, evaluated through a comprehensive 8760-hour simulation over a 20-year planning horizon. The evaluation is further enhanced by a set of refined Algorithm Performance Evaluation Metrics (AL-PEM) tailored to the specific constraints. The findings not only underscore the robustness and consistency of the SPEA2 variant over 15 runs of 200 generations each, which ranks first on the AL-PEM scale, but the findings also validate the strategic merit of combining multiple technologies and empowering policymakers with a versatile toolkit for informed decision-making.

关键词： sustainable energy solutions renewable energy integration multi-criteria decision tool advanced computational techniques grid-connected hybrid system optimization algorithms policy decision-making metrics environmental sustainability energy security

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Application of ANN control algorithm for optimizing performance of a hybrid ORC power plant

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ENERGY 2024年 306卷

作者： Podlasek, Szymon Jankowski, Marcin Balazy, Patryk Lalik, Krzysztof Figaj, Rafal AGH Univ Krakow Fac Mech Engn & Robot Al Mickiewicza 30 PL-30059 Krakow Poland AGH Univ Krakow Fac Energy & Fuels Al Mickiewicza 30 PL-30059 Krakow Poland

Hybrid systems for generating electricity from multiple sources are becoming an increasingly popular subject of analysis in science and industry. This paper presents a validated model of a hybrid ORC plant powered by solar and geothermal energy. A key challenge in optimizing the operating parameters over time was the variability of solar conditions, which was the main energy source of the system. The operation of the ORC plant is simulated using a complex model with Multiple Input Multiple Output (MIMO) variables, which is nonlinear. The input variables represent the system's operational parameters, while the output variables describe the plant's performance indicators. The main objective of this paper is to optimize the year-round performance of the ORC installation through different computational techniques. The first approach involves the application of the gradient-based optimization method that is known as sequential quadratic programming (SQP). With the use of SQP, two distinct simulation runs (SQP-N and SQP-Q/N) of the system are performed, each with a specific objective function to be optimized. The second approach is based on reinforcement learning principles and leverages the method known as Deep Deterministic Policy Gradient (DDPG) algorithm. The main advantage of DDPG over SQP is that DDPG does not require knowledge of the model. This improves the algorithm flexibility, making it well-adapted to fluctuating environmental conditions. Overall, three optimization runs (two using SQP, one using DDPG) have been performed, aiming at identifying the optimal year-round control strategy for the installation. The results revealed that under the control of DDPG, the hybrid system has produced the highest amount of electricity (4993.4 MWh), outperforming in this matter SQP-N and SQP-Q/N optimization variants by 16.83 % and 10.49%, respectively.

关键词： Hybrid energy systems Renewable energy sources Neural networks optimization algorithms Computer modeling

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Optimizing energy Dynamics: A comprehensive analysis of hybrid energy storage systems integrating battery banks and supercapacitors

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ENERGY CONVERSION AND MANAGEMENT 2024年 312卷

作者： Guven, Aykut Fatih Abdelaziz, Almoataz Y. Samy, Mohamed Mahmoud Barakat, Shimaa Yalova Univ Engn Fac Dept Elect & Elect Engn Yalova Turkiye Ain Shams Univ Fac Engn Cairo 11517 Egypt Future Univ Egypt Fac Engn & Technol Cairo 11835 Egypt Beni Suef Univ Dept Elect Engn Bani Suwayf Egypt

This study investigates the optimization of a grid-connected hybrid energy system integrating photovoltaic (PV) and wind turbine (WT) components alongside battery and supercapacitor storage. The research addresses the critical need for efficient energy storage solutions in renewable energy integration. Six optimization algorithms-AGTO, ARO, BOA, CGO, PFA, and TSO-are evaluated for their efficacy in determining optimal system configurations. The system's adaptability to dynamic scenarios is examined through comprehensive sensitivity analyses, shedding light on its robustness. The findings reveal that the CGO algorithm outperforms others by achieving optimal solutions with fewer iterations, highlighting its efficiency. Key conclusions include the identification of an optimal configuration comprising a 589.58 kW PV system, 664 kW WT, a 675-kW supercapacitor, and a 1000 kWh battery bank. This configuration achieves an 80 % renewable energy fraction (REF), reduces the annual system cost (ACS) to $603,537.8522, and maintains a competitive levelized cost of electricity (LCOE) at $0.2380 per kWh. The research underscores the significance of integrated energy storage solutions in optimizing hybrid energy configurations, offering insights crucial for advancing sustainable energy initiatives. The study contributes valuable insights to the scientific community, paving the way for more efficient and resilient renewable energy systems.

关键词： Hybrid renewable energy system Hybrid energy storage system Supercapacitor optimization algorithms Sensitivity Analysis Sustainable energy

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Improving the Accuracy of Neural Network Pattern Recognition by Fractional Gradient Descent

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IEEE ACCESS 2024年 12卷 168428-168444页

作者： Abdulkadirov, Ruslan I. Lyakhov, Pavel A. Baboshina, Valentina A. Nagornov, Nikolay N. North Caucasus Fed Univ North Caucasus Ctr Math Res Stavropol 355017 Russia North Caucasus Fed Univ Dept Math Modeling Stavropol 355017 Russia

In this paper we propose the fractional gradient descent for increasing the training and work of modern neural networks. This optimizer searches the global minimum of the loss function considering the fractional gradient directions achieved by Riemann-Liouville, Caputo, and Grunwald-Letnikov derivatives. The adjusting of size and direction of the fractional gradient, supported by momentum and Nesterov condition, let the proposed optimizer descend into the global minimum of loss functions of neural networks. Utilizing the proposed optimization algorithm in a linear neural network and a visual transformer lets us attain higher accuracy, precision, recall, Macro F1 score by 1.8-4 percentage points than known analogs than state-of-the-art methods in solving pattern recognition problems on images from MNIST and CIFAR10 datasets. Further research of fractional calculus in modern neural network methodology can improve the quality of solving various challenges such as pattern recognition, time series forecasting, moving object detection, and data generation.

关键词： Neural networks optimization Pattern recognition Accuracy Convergence Training Transformers Heuristic algorithms Stability analysis Multilayer perceptrons Convolutional neural networks fractional derivatives of Riemann-Liouville Caputo Grunwald-Letnikov multilayer perceptron optimization algorithms stochastic gradient descent

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Review of Modeling, Modulation, and Control Strategies for the Dual-Active-Bridge DC/DC Converter

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ENERGIES 2023年第18期16卷 6646页

作者： He, Jiayang Chen, Yangyu Lin, Jiongtao Chen, Jianghui Cheng, Li Wang, Yu Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Zhongkai Univ Agr & Engn Coll Automat Guangzhou 510225 Peoples R China

This paper provides a comprehensive review of the existing research on the Dual Active Bridge (DAB) DC-DC converter, focusing on modeling methods, modulation strategies, optimization algorithms, and control methods. A comparative analysis of selected methods along with guidelines to assist engineers and researchers in their study of DAB is also presented. Firstly, a comprehensive review of modulation strategies for DAB is provided, ranging from classical phase-shift modulation to the popular asymmetric duty modulation. The intrinsic relationships among different modulation methods are summarized, and a comparison is made based on the difficulty of control and DAB operating characteristics. Secondly, the various modeling methods for DAB are described, including reduced-order modeling, generalized state-space averaging modeling, and discrete-time modeling methods. A comparison is made based on the suitability for different application scenarios, providing recommendations for the adoption of different modeling methods. Furthermore, a survey of optimization algorithms for modulation methods is presented, including classical algorithms, swarm intelligence optimization, and reinforcement learning algorithms. A number of criteria are proposed for different algorithms, and an analysis of the unresolved challenges and future prospects is provided. Finally, the advanced control methods for DAB are summarized based on control effectiveness and applicability. The article concludes with a summary and an outlook on future research directions is also provided.

关键词： dual active bridge (DAB) modeling methods modulation strategies optimization algorithms advanced control methods

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