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Keywords = differential evolution algorithm (DEA)

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5 pages, 569 KB  
Proceeding Paper
Hybrid Modelling Framework for Reactor Model Discovery Using Artificial Neural Networks Classifiers
by Emmanuel Agunloye, Asterios Gavriilidis and Federico Galvanin
Proceedings 2025, 121(1), 11; https://doi.org/10.3390/proceedings2025121011 - 25 Jul 2025
Viewed by 542
Abstract
Developing and identifying the correct reactor model for a reaction system characterized by a high number of reaction pathways and flow regimes can be challenging. In this work, artificial neural networks (ANNs), used in deep learning, are used to develop a hybrid modelling [...] Read more.
Developing and identifying the correct reactor model for a reaction system characterized by a high number of reaction pathways and flow regimes can be challenging. In this work, artificial neural networks (ANNs), used in deep learning, are used to develop a hybrid modelling framework for physics-based model discovery in reactions systems. The model discovery accuracy of the framework is investigated considering kinetic model parametric uncertainty, noise level, features in the data structure and experimental design optimization via a differential evolution algorithm (DEA). The hydrodynamic behaviours of both a continuously stirred tank reactor and a plug flow reactor and rival chemical kinetics models are combined to generate candidate physics-based models to describe a benzoic acid esterification synthesis in a rotating cylindrical reactor. ANNs are trained and validated from in silico data simulated by sampling the parameter space of the physics-based models. Results show that, when monitored using test data classification accuracy, ANN performance improved when the kinetic parameters uncertainty decreased. The performance improved further by increasing the number of features in the data set, optimizing the experimental design and decreasing the measurements error (low noise level). Full article
(This article belongs to the Proceedings of The 1st SUSTENS Meeting)
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21 pages, 1652 KB  
Article
Comparative Study of White Shark Optimization and Combined Meta-Heuristic Algorithm for Enhanced MPPT in Photovoltaic Systems
by Fajar Kurnia Al Farisi, Zhi-Kai Fan and Kuo-Lung Lian
Energies 2025, 18(8), 2110; https://doi.org/10.3390/en18082110 - 19 Apr 2025
Cited by 1 | Viewed by 969
Abstract
This paper proposes a novel hybrid metaheuristic algorithm (MHA) for maximum power point tracking (MPPT), integrating particle swarm optimization (PSO), the differential evolution algorithm (DEA), and the grey wolf optimizer (GWO). The proposed method is inspired by the structural phases of the white [...] Read more.
This paper proposes a novel hybrid metaheuristic algorithm (MHA) for maximum power point tracking (MPPT), integrating particle swarm optimization (PSO), the differential evolution algorithm (DEA), and the grey wolf optimizer (GWO). The proposed method is inspired by the structural phases of the white shark optimizer (WSO), a recently introduced MHA. This study evaluates the MPPT performance of WSO and compares it with the proposed hybrid approach to provide insights into optimal MPPT selection. The key contributions include an in-depth analysis of the WSO framework, benchmarking its performance against the hybrid model. Both algorithms are implemented in an MPPT system and assessed based on tracking speed, accuracy, and adaptability. The results indicate that the WSO achieves a faster convergence due to its biologically inspired design, whereas the hybrid model, despite requiring additional coordination time, ensures comprehensive search space exploration. Notably, the proposed method excels in dynamic tracking efficiency, which is crucial for accurately following time-varying P-V curves. This study underscores the trade-off between tracking speed and efficiency, demonstrating that while WSO is advantageous for rapid tracking, the hybrid approach enhances overall MPPT performance under dynamic conditions. These findings offer valuable insights for optimizing MPPT strategies in renewable energy systems. Full article
(This article belongs to the Section A: Sustainable Energy)
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18 pages, 3705 KB  
Article
A Simple Control Strategy for Planar 2R Underactuated Robot via DEA Optimization
by Zixin Huang, Xiangyu Gong, Xiao Wan and Hongjian Zhou
Actuators 2025, 14(3), 156; https://doi.org/10.3390/act14030156 - 20 Mar 2025
Viewed by 556
Abstract
In various fields, planar 2R underactuated robots have garnered significant attention due to their numerous applications. To guarantee the stable control of these robots, a simple control strategy is presented in this paper, and we utilize the intelligent optimization algorithm to enhance the [...] Read more.
In various fields, planar 2R underactuated robots have garnered significant attention due to their numerous applications. To guarantee the stable control of these robots, a simple control strategy is presented in this paper, and we utilize the intelligent optimization algorithm to enhance the controller parameters. Initially, a comprehensive dynamic model is developed for the robot with its control properties described. Subsequently, we design a PD controller to control the movement of the planar 2R underactuated robot. The differential evolution algorithm (DEA) is used to optimize the parameters of the PD controller to obtain the best control effect and make each link reach the target state. The findings from the simulation demonstrate the efficacy of the approach, and the designed strategy shows a higher stability and convergence rate, highlighting its important contribution to the field of underactuated robots. Full article
(This article belongs to the Special Issue Modeling and Nonlinear Control for Complex MIMO Mechatronic Systems)
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18 pages, 2959 KB  
Article
Parameter Identification in Triple-Diode Photovoltaic Modules Using Hybrid Optimization Algorithms
by Dhiaa Halboot Muhsen, Haider Tarish Haider and Yaarob Al-Nidawi
Designs 2024, 8(6), 119; https://doi.org/10.3390/designs8060119 - 12 Nov 2024
Cited by 1 | Viewed by 1238
Abstract
Identifying the parameters of a triple-diode electrical circuit structure in PV modules is a critical issue, and it has been regarded as an important research area. Accordingly, in this study, a differential evolution algorithm (DEA) is hybridized with an electromagnetism-like algorithm (EMA) in [...] Read more.
Identifying the parameters of a triple-diode electrical circuit structure in PV modules is a critical issue, and it has been regarded as an important research area. Accordingly, in this study, a differential evolution algorithm (DEA) is hybridized with an electromagnetism-like algorithm (EMA) in the mutation stage to enhance the reliability and efficiency of the DEA. A new formula is presented to adapt the control parameters (mutation factor and crossover rate) of the DEA. Seven different experimental data sets are used to improve the performance of the proposed differential evolution with an integrated mutation per iteration algorithm (DEIMA). The results of the proposed PV modeling method are evaluated with other state-of-the-art approaches. According to different statistical criteria, the DEIMA demonstrates superiority in terms of root mean square error and main bias error by at least 5.4% and 10%, respectively, as compared to other methods. Furthermore, the DEIMA has an average execution time of 27.69 s, which is less than that of the other methods. Full article
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12 pages, 443 KB  
Article
Two-Stage Control Strategy Based on Motion Planning for Planar Prismatic–Rotational Underactuated Robot
by Dawei Li, Ziang Wei and Zixin Huang
Actuators 2024, 13(8), 278; https://doi.org/10.3390/act13080278 - 25 Jul 2024
Cited by 1 | Viewed by 1449
Abstract
Intelligent robots are often used to explore various areas instead of humans. However, when the driving joint is damaged, the actuated robot degenerates to an underactuated robot, and the traditional control method is not suitable for the underactuated robot. In this work, a [...] Read more.
Intelligent robots are often used to explore various areas instead of humans. However, when the driving joint is damaged, the actuated robot degenerates to an underactuated robot, and the traditional control method is not suitable for the underactuated robot. In this work, a two-stage control approach for a planar prismatic–rotational (PR) underactuated robot is introduced. Firstly, we establish the dynamic model and describe the underactuated constraint between an underactuated rotational joint and active prismatic joint. Secondly, the trajectory with multiple parameters is planned to ensure that the two joints reach the target position. Based on underactuated constraints and the evaluation function, the differential evolution algorithm (DEA) is used to optimize these parameters. After that, in stage 1, we design the controller to move the active prismatic joint to the desired position. Meanwhile, the underactuated rotational joint is rotating freely. In stage 2, we design the controller for the active prismatic joint to track the planned trajectory. By means of this strategy, both joints reach their target locations simultaneously. The final simulation result demonstrates that this strategy is effective. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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21 pages, 4980 KB  
Article
Extracting Accurate Parameters from a Proton Exchange Membrane Fuel Cell Model Using the Differential Evolution Ameliorated Meta-Heuristics Algorithm
by Badreddine Kanouni and Abdelbaset Laib
Energies 2024, 17(10), 2333; https://doi.org/10.3390/en17102333 - 12 May 2024
Cited by 11 | Viewed by 1996
Abstract
The electrochemical proton exchange membrane fuel cell (PEMFC) is an electrical generator that utilizes a chemical reaction mechanism to produce electricity, serving as a sustainable and environmentally friendly energy source. To thoroughly analyze and develop the features and performance of a PEMFC, it [...] Read more.
The electrochemical proton exchange membrane fuel cell (PEMFC) is an electrical generator that utilizes a chemical reaction mechanism to produce electricity, serving as a sustainable and environmentally friendly energy source. To thoroughly analyze and develop the features and performance of a PEMFC, it is essential to use a precise model that incorporates exact parameters to effectively suit the polarization curve. In addition, parameter extraction plays a crucial role in the simulation analysis, evaluation, optimum control, and fault detection of the proton exchange membrane fuel cell (PEMFC) system. Despite the development of many algorithms for parameter extraction in PEMFC, obtaining accurate and trustworthy results rapidly remains a challenge. This study presents a hybridized algorithm, namely differential evolution ameliorated (DEA) for reliably estimating PEMFC model parameters. To evaluate the proposed DEA-based parameter identification, a comparison analysis with previously published methods is conducted using MATLAB/SimulinkTM (R2016b, MathWorks, Natick, MA, USA) in terms of system correctness and convergence process. The proposed DEA algorithm is tested to extract the parameters of two PEMFC models: SR-12 500 W and 250 W. The sum of the squared errors (SSE) between the experimental and the obtained voltage data is defined as an objective function. The simulation results prove that the suggested DEA algorithm is capable of identifying the optimal PEMFC parameters rapidly and accurately in comparison with other optimization algorithms. Full article
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15 pages, 14687 KB  
Article
An Efficient Method for Wavefront Aberration Correction Based on the RUN Optimizer
by Huizhen Yang, Xiangdong Zang, Peng Chen, Xingliu Hu, Yongqiang Miao, Zhaojun Yan and Zhiguang Zhang
Photonics 2024, 11(1), 29; https://doi.org/10.3390/photonics11010029 - 28 Dec 2023
Cited by 3 | Viewed by 2098
Abstract
The correction of wavefront aberrations in wavefront sensorless (WFS-less) adaptive optical (AO) systems requires control algorithms that can ensure rapid convergence while maintaining effective correction capabilities. This paper proposes a novel control algorithm based on the RUNge Kutta optimizer (RUN) for WFS-less AO [...] Read more.
The correction of wavefront aberrations in wavefront sensorless (WFS-less) adaptive optical (AO) systems requires control algorithms that can ensure rapid convergence while maintaining effective correction capabilities. This paper proposes a novel control algorithm based on the RUNge Kutta optimizer (RUN) for WFS-less AO systems that enables the quick and efficient correction of small aberrations, as well as larger aberrations. To evaluate the convergence speed and correction capabilities of a WFS-less AO system based on the RUN control algorithm, we constructed a simulated AO system and an experimental setup with a 97-element deformable mirror (DM), respectively. Additionally, the results obtained with the Particle Swarm Optimization (PSO) algorithm, Differential Evolution Algorithm (DEA), and Genetic Algorithm (GA) are also provided for comparison and analysis. Both the simulated and experimental results consistently demonstrated that our proposed method outperformed several competing algorithms in terms of correction performance and convergence speed. Furthermore, the experimental results further validate the effectiveness of our control algorithm in scenarios involving significant aberrations. Full article
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22 pages, 848 KB  
Article
An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid
by Hisham Alghamdi, Ghulam Hafeez, Sajjad Ali, Safeer Ullah, Muhammad Iftikhar Khan, Sadia Murawwat and Lyu-Guang Hua
Mathematics 2023, 11(21), 4561; https://doi.org/10.3390/math11214561 - 6 Nov 2023
Cited by 13 | Viewed by 2394
Abstract
Accurate load forecasting plays a crucial role in the effective energy management of smart cities. However, the smart cities’ residents’ load profile is nonlinear, having high volatility, uncertainty, and randomness. Forecasting such nonlinear profiles requires accurate and stable prediction models. On this note, [...] Read more.
Accurate load forecasting plays a crucial role in the effective energy management of smart cities. However, the smart cities’ residents’ load profile is nonlinear, having high volatility, uncertainty, and randomness. Forecasting such nonlinear profiles requires accurate and stable prediction models. On this note, a prediction model has been developed by combining feature preprocessing, a multilayer perceptron, and a genetic wind-driven optimization algorithm, namely FPP-MLP-GWDO. The developed hybrid model has three parts: (i) feature preprocessing (FPP), (ii) a multilayer perceptron (MLP), and (iii) a genetic wind-driven optimization (GWDO) algorithm. The MLP is the key part of the developed model, which uses a multivariate autoregressive algorithm and rectified linear unit (ReLU) for network training. The developed hybrid model known as FPP-MLP-GWDO is evaluated using Dayton Ohio grid load data regarding aspects of accuracy (the mean absolute percentage error (MAPE), Theil’s inequality coefficient (TIC), and the correlation coefficient (CC)) and convergence speed (computational time (CT) and convergence rate (CR)). The findings endorsed the validity and applicability of the developed model compared to other literature models such as the feature selection–support vector machine–modified enhanced differential evolution (FS-SVM-mEDE) model, the feature selection–artificial neural network (FS-ANN) model, the support vector machine–differential evolution algorithm (SVM-DEA) model, and the autoregressive (AR) model regarding aspects of accuracy and convergence speed. The findings confirm that the developed FPP-MLP-GWDO model achieved an accuracy of 98.9%, thus surpassing benchmark models such as the FS-ANN (96.5%), FS-SVM-mEDE (97.9%), SVM-DEA (97.5%), and AR (95.7%). Furthermore, the FPP-MLP-GWDO significantly reduced the CT (299s) compared to the FS-SVM-mEDE (350s), SVM-DEA (240s), FS-ANN (159s), and AR (132s) models. Full article
(This article belongs to the Special Issue Heuristic Optimization and Machine Learning)
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23 pages, 7251 KB  
Article
Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification
by Hasnat Bin Tariq, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema and Ahmad H. Milyani
Mathematics 2021, 9(24), 3199; https://doi.org/10.3390/math9243199 - 11 Dec 2021
Cited by 4 | Viewed by 2504
Abstract
Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is [...] Read more.
Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence. Full article
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15 pages, 2883 KB  
Article
Cost Minimizations and Performance Enhancements of Power Systems Using Spherical Prune Differential Evolution Algorithm Including Modal Analysis
by Sherif S. M. Ghoneim, Mohamed F. Kotb, Hany M. Hasanien, Mosleh M. Alharthi and Attia A. El-Fergany
Sustainability 2021, 13(14), 8113; https://doi.org/10.3390/su13148113 - 20 Jul 2021
Cited by 8 | Viewed by 2623
Abstract
A novel application of the spherical prune differential evolution algorithm (SpDEA) to solve optimal power flow (OPF) problems in electric power systems is presented. The SpDEA has several merits, such as its high convergence speed, low number of parameters to be designed, and [...] Read more.
A novel application of the spherical prune differential evolution algorithm (SpDEA) to solve optimal power flow (OPF) problems in electric power systems is presented. The SpDEA has several merits, such as its high convergence speed, low number of parameters to be designed, and low computational procedures. Four objectives, complete with their relevant operating constraints, are adopted to be optimized simultaneously. Various case studies of multiple objective scenarios are demonstrated under MATLAB environment. Static voltage stability index of lowest/weak bus using modal analysis is incorporated. The results generated by the SpDEA are investigated and compared to standard multi-objective differential evolution (MODE) to prove their viability. The best answer is chosen carefully among trade-off Pareto points by using the technique of fuzzy Pareto solution. Two power system networks such as IEEE 30-bus and 118-bus systems as large-scale optimization problems with 129 design control variables are utilized to point out the effectiveness of the SpDEA. The realized results among many independent runs indicate the robustness of the SpDEA-based approach on OPF methodology in optimizing the defined objectives simultaneously. Full article
(This article belongs to the Special Issue Advanced Renewable Energy for Sustainability)
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39 pages, 5577 KB  
Article
Optimal Planning of Integrated Nuclear-Renewable Energy System for Marine Ships Using Artificial Intelligence Algorithm
by Hossam A. Gabbar, Md. Ibrahim Adham and Muhammad R. Abdussami
Energies 2021, 14(11), 3188; https://doi.org/10.3390/en14113188 - 29 May 2021
Cited by 19 | Viewed by 4492
Abstract
Ocean-going ships are one of the primary sources of Greenhouse Gas (GHG) emissions. Several actions are being taken to reduce the GHG emissions from maritime vessels, and integration of Renewable Energy Sources (RESs) is one of them. Ocean-going marine ships need a large [...] Read more.
Ocean-going ships are one of the primary sources of Greenhouse Gas (GHG) emissions. Several actions are being taken to reduce the GHG emissions from maritime vessels, and integration of Renewable Energy Sources (RESs) is one of them. Ocean-going marine ships need a large amount of reliable energy to support the propulsive load. Intermittency is one of the drawbacks of RESs, and penetration of RESs in maritime vessels is limited by the cargo carrying capacity and usable area of that ship. Other types of reliable energy sources need to be incorporated in ships to overcome these shortcomings of RESs. Some researchers proposed to integrate fossil fuel-based generators like diesel generators and renewable energy in marine vessels to reduce GHG emissions. As the penetration of RESs in marine ships is limited, fossil fuel-based generators provide most of the energy. Therefore, renewable and fossil fuel-based hybrid energy systems in maritime vessels can not reduce GHG emissions to the desired level. Fossil fuel-based generators need to be replaced by emissions-free energy sources to make marine ships free from emissions. Nuclear energy is emissions-free energy, and small-scale nuclear reactors like Microreactors (MRs) are competent to replace fossil fuel-based generators. In this paper, the technical, environmental, and economic competitiveness of Nuclear-Renewable Hybrid Energy Systems (N-R HES) in marine ships are assessed. The lifecycle cost of MR, reliability of the proposed system, and limitations of integrating renewable energy in maritime vessels are considered in this study. The proposed N-R HES is compared with three different energy systems, namely ‘Standalone Fossil Fuel-based Energy Systems’, ‘Renewable and Fossil Fuel-based Hybrid Energy Systems’, and ‘Standalone Nuclear Energy System’. The cost modeling of each energy system is carried out in MATLAB simulator. Each energy system is optimized by using the Differential Evolution Algorithm (DEA), an artificial intelligence algorithm, to find out the optimal configuration of the system components in terms of Net Present Cost (NPC). The results determine that N-R HES has the lowest NPC compared to the other three energy systems. The performance of the DE algorithm is compared with another widely accepted artificial intelligence optimization technique called ‘Particle Swarm Optimization (PSO)’ to validate the findings of the DE algorithm. The impact of control parameters in the DE algorithm is assessed by employing the Adaptive Differential Evolution (ADE) algorithm. A sensitivity analysis is carried out to assess the impact of different system parameters on this study’s findings. Full article
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22 pages, 3930 KB  
Article
Optimization Model for Biogas Power Plant Feedstock Mixture Considering Feedstock and Transportation Costs Using a Differential Evolution Algorithm
by Danijel Topić, Marinko Barukčić, Dražen Mandžukić and Cecilia Mezei
Energies 2020, 13(7), 1610; https://doi.org/10.3390/en13071610 - 1 Apr 2020
Cited by 9 | Viewed by 3014
Abstract
In this paper, an optimization model for biogas power plant feedstock mixture with respect to feedstock and transportation costs using a differential evolution algorithm (DEA) is presented. A mathematical model and an optimization problem are presented. The proposed model introduces an optimal mixture [...] Read more.
In this paper, an optimization model for biogas power plant feedstock mixture with respect to feedstock and transportation costs using a differential evolution algorithm (DEA) is presented. A mathematical model and an optimization problem are presented. The proposed model introduces an optimal mixture of different feedstock combinations in a biogas power plant and informs about the maximal transportation distance for each feedstock before being unprofitable. In the case study, the proposed model is applied to five most commonly used feedstock in biogas power plants in Croatia and Hungary. The research is performed for a situation when the biogas power plant is not owned by the farm owner but by a third party. An optimization procedure is performed for each scenario with a cost of methane production that does not exceed 0.75 EUR/m3 in 1 MWe biogas power plant. The results show the needed yearly amounts and the maximum transportation distance of each feedstock. Full article
(This article belongs to the Section L: Energy Sources)
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16 pages, 1545 KB  
Article
Optimal Energy Management of Railroad Electrical Systems with Renewable Energy and Energy Storage Systems
by Seunghyun Park and Surender Reddy Salkuti
Sustainability 2019, 11(22), 6293; https://doi.org/10.3390/su11226293 - 8 Nov 2019
Cited by 49 | Viewed by 5035
Abstract
The proposed optimal energy management system balances the energy flows among the energy consumption by accelerating trains, energy production from decelerating trains, energy from wind and solar photovoltaic (PV) energy systems, energy storage systems, and the energy exchange with a traditional electrical grid. [...] Read more.
The proposed optimal energy management system balances the energy flows among the energy consumption by accelerating trains, energy production from decelerating trains, energy from wind and solar photovoltaic (PV) energy systems, energy storage systems, and the energy exchange with a traditional electrical grid. In this paper, an AC optimal power flow (AC-OPF) problem is formulated by optimizing the total cost of operation of a railroad electrical system. The railroad system considered in this paper is composed of renewable energy resources such as wind and solar PV systems, regenerative braking capabilities, and hybrid energy storage systems. The hybrid energy storage systems include storage batteries and supercapacitors. The uncertainties associated with wind and solar PV powers are handled using probability distribution functions. The proposed optimization problem is solved using the differential evolution algorithm (DEA). The simulation results show the suitability and effectiveness of proposed approach. Full article
(This article belongs to the Section Sustainable Transportation)
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17 pages, 4479 KB  
Article
A Novel Damage Indicator Based on the Electromechanical Impedance Principle for Structural Damage Identification
by Pin Zhou, Dansheng Wang and Hongping Zhu
Sensors 2018, 18(7), 2199; https://doi.org/10.3390/s18072199 - 8 Jul 2018
Cited by 19 | Viewed by 3506
Abstract
This paper presents a novel structural damage detection indicator, i.e., fourth-order voltage statistical moment (FVSM) based on the electromechanical impedance (EMI) principle, and then proposes a two-step damage detection method based on the novel indicator and a differential evolution algorithm (DEA). In this [...] Read more.
This paper presents a novel structural damage detection indicator, i.e., fourth-order voltage statistical moment (FVSM) based on the electromechanical impedance (EMI) principle, and then proposes a two-step damage detection method based on the novel indicator and a differential evolution algorithm (DEA). In this study, several lead zirconate titanate (PZT) sensors bonded to an experimental steel beam were utilized to acquire the time-domain voltage responses. On this basis, the fourth-order voltage statistical moments (FVSMs) of the voltage responses are computed to locate the damage element in the detected structure, and the proposed damage detection method is utilized to quantify the damage. In addition, theoretical PZT voltage responses are also calculated based on the piezoelectric theory and the spectral element method (SEM). Experimental results verify the accuracy of the theoretical voltage values and the effectiveness of the proposed damage indicator. Results indicate that the FVSM is effective in locating the damage element. Integrated with DEA, the proposed technique is capable of quantifying damage. Full article
(This article belongs to the Section Physical Sensors)
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