Golden Section Search Algorithm Research Articles

Enhanced LaRC05 failure criteria for investigating low-velocity impact on fiber-reinforced composites: An experimental and computational study

A finite element model was developed using both continuum and discrete damage modeling techniques to provide detailed predictions for ply-by-ply damage progression in composite laminates during low-velocity impact (LVI) events. A new fiber failure model was incorporated into the LaRC05 failure criteria to predict fiber pull-out and fiber crushing during the fiber damage evolution. In addition, the selective range golden section search (SRGSS) algorithm was implemented to efficiently predict fiber breakage, pull-out, splitting, kinking and crushing, and matrix cracking. The delamination was captured by cohesive element layers embedded between every adjacent composite ply. The interactions of intralaminar matrix cracking and delamination were modeled by deploying cohesive elements within each composite ply. The prediction results were validated by 30 J and 75 J drop-weight tests with different-sized impactors, as well as X-Ray CT inspections on 254 mm by 304.8 mm [0/45/90/-45]4s IM7/977–3 laminates. The model predicted the maximum deflection and contact duration with <2 % error, and the peak load, damaged areas, and absorbed energy with <8 % error. The matrix fracture plane and the fiber kink band angle were found with 1° precision 48 % faster via the SRGSS algorithm. The detailed sequences of damage occurrence were predicted by analyzing the energy dissipation histories through various damage modes. Although this modeling methodology was developed for LVI scenarios, it has broad applications for predicting failures in composites.

Optimal Combination of the Splitting–Linearizing Method to SSOR and SAOR for Solving the System of Nonlinear Equations

The symmetric successive overrelaxation (SSOR) and symmetric accelerated overrelaxation (SAOR) are conventional iterative methods for solving linear equations. In this paper, novel approaches are presented by combining a splitting–linearizing method with SSOR and SAOR for solving a system of nonlinear equations. The nonlinear terms are decomposed at two sides through a splitting parameter, which are linearized around the values at the previous step, obtaining a linear equation system at each iteration step. The optimal values of parameters are determined to minimize the reciprocal of the maximal projection, which are sought in preferred ranges using the golden section search algorithm. Numerical tests assess the performance of the developed methods, namely, the optimal splitting symmetric successive over-relaxation (OSSSOR), and the optimal splitting symmetric accelerated over-relaxation (OSSAOR). The chief advantages of the proposed methods are that they do not need to compute the inverse matrix at each iteration step, and the computed orders of convergence by OSSSOR and OSSAOR are between 1.5 and 5.61; they, without needing the inner iterations loop, converge very fast with saving CPU time to find the true solution with a high accuracy.

Lithium-Ion Supercapacitors and Batteries for Off-Grid PV Applications: Lifetime and Sizing

The intermittent nature of power generation from photovoltaics (PV) requires reliable energy storage solutions. Using the storage system outdoors exposes it to variable temperatures, affecting both its storage capacity and lifespan. Utilizing and optimizing energy storage considering climatic variations and new storage technologies is still a research gap. Therefore, this paper presents a modified sizing algorithm based on the Golden Section Search method, aimed at optimizing the number of cells in an energy storage unit, with a specific focus on the unique conditions of Denmark. The considered energy storage solutions are Lithium-ion capacitors (LiCs) and Lithium-ion batteries (LiBs), which are tested under different temperatures and C-rates rates. The algorithm aims to maximize the number of autonomy cycles—defined as periods during which the system operates independently of the grid, marked by intervals between two consecutive 0% State of Charge (SoC) occurrences. Testing scenarios include dynamic temperature and dynamic load, constant temperature at 25 °C, and constant load, considering irradiation and temperature effects and cell capacity fading over a decade. A comparative analysis reveals that, on average, the LiC storage is sized at 70–80% of the LiB storage across various scenarios. Notably, under a constant-temperature scenario, the degradation rate accelerates, particularly for LiBs. By leveraging the modified Golden Section Search algorithm, this study provides an efficient approach to the sizing problem, optimizing the number of cells and thus offering a potential solution for energy storage in off-grid PV systems.

Variable optimization domain-based cooperative energy management strategy for connected plug-in hybrid electric vehicles

The design of energy management strategy (EMS) that can be applied in real-time with nearly optimal fuel economy for connected plug-in hybrid electric vehicles (C-PHEVs) is an urgent need at present, especially in the context where the benefits of rapid development of intelligent transportation system are increasingly evident. Equivalent consumption minimization strategy (ECMS) is able to achieve the desired performance, on the premise that the equivalent factor (EF) is adjusted reasonably. To achieve this goal, a variable optimization domain-based cooperative EMS for C-PHEVs is proposed in this paper. First, an offline sub-cycle division method is designed, which is effectively utilized to construct a fitting function to output reference EF based on the latest driving information. Second, the theoretical relationship between EF and operating efficiency of the driving components is explored, and the variable optimization domain of EF is designed to avoid inefficient operation of engine. Third, the EF optimization is then simplified into a quadratic problem within the designed domain, which is rapidly solved online with the golden section search algorithm. Finally, the comparison work is conducted under two real-world driving cycles. The results exhibit that the proposed strategy improves the fuel economy of C-PHEV by 6.440 % and 7.936 % over that using the conventional adaptive ECMS (CA-ECMS), respectively. The average engine fuel consumption rates of the proposed strategy are significantly reduced compared with that of CA-ECMS. Moreover, the effectiveness of the proposed strategy is verified on the experiment platform, demonstrating its application prospects.

Current sensor-based single MPPT controller using sequential golden section search algorithm for hybrid solar PV generator-TEG in isolated DC microgrid

A current sensor-based single maximum power point tracking (SMPPT) controller is proposed for extracting the maximum power (MP) from a hybrid solar photovoltaic (PV) generator-thermoelectric generator (TEG) supplying an isolated DC microgrid. The proposed SMPPT controller tracks the maximum power points (MPPs) of the hybrid solar PV generator-TEG using the sequential golden section search (SGSS) algorithm. Faster and guaranteed convergence are the major advantages of this SGSS algorithm for tracking the MPPs of hybrid solar PV generator-TEG sequentially. Further, the proposed SMPPT controller requires a single sensing and signal conditioning circuit (SSCC) and a digital controller for successful operation. Thus, it requires less investment cost, reduces control complexity, consumes less power, and improves reliability. Extensive simulations, experiments, and comparative studies have demonstrated the effectiveness of the proposed SMPPT controller using the SGSS algorithm.

Automatic search for photoacoustic marker using automated transrectal ultrasound.

Real-time transrectal ultrasound (TRUS) image guidance during robot-assisted laparoscopic radical prostatectomy has the potential to enhance surgery outcomes. Whether conventional or photoacoustic TRUS is used, the robotic system and the TRUS must be registered to each other. Accurate registration can be performed using photoacoustic (PA markers). However, this requires a manual search by an assistant [IEEE Robot. Autom. Lett8, 1287 (2023).10.1109/LRA.2022.3191788]. This paper introduces the first automatic search for PA markers using a transrectal ultrasound robot. This effectively reduces the challenges associated with the da Vinci-TRUS registration. This paper investigated the performance of three search algorithms in simulation and experiment: Weighted Average (WA), Golden Section Search (GSS), and Ternary Search (TS). For validation, a surgical prostate scenario was mimicked and various ex vivo tissues were tested. As a result, the WA algorithm can achieve 0.53°±0.30° average error after 9 data acquisitions, while the TS and GSS algorithm can achieve and 0.48°±0.32° average errors after 28 data acquisitions.

Regularized Normalization Methods for Solving Linear and Nonlinear Eigenvalue Problems

To solve linear and nonlinear eigenvalue problems, we develop a simple method by directly solving a nonhomogeneous system obtained by supplementing a normalization condition on the eigen-equation for the uniqueness of the eigenvector. The novelty of the present paper is that we transform the original homogeneous eigen-equation to a nonhomogeneous eigen-equation by a normalization technique and the introduction of a simple merit function, the minimum of which leads to a precise eigenvalue. For complex eigenvalue problems, two normalization equations are derived utilizing two different normalization conditions. The golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues, and simultaneously, we can obtain precise eigenvectors to satisfy the eigen-equation. Two regularized normalization methods can accelerate the convergence speed for two extensions of the simple method, and a derivative-free fixed-point Newton iterative scheme is developed to compute real eigenvalues, the convergence speed of which is ten times faster than the golden section search algorithm. Newton methods are developed for solving two systems of nonlinear regularized equations, and the efficiency and accuracy are significantly improved. Over ten examples demonstrate the high performance of the proposed methods. Among them, the two regularization methods are better than the simple method.

Dynamical Optimal Values of Parameters in the SSOR, AOR, and SAOR Testing Using Poisson Linear Equations

This paper proposes a dynamical approach to determine the optimal values of the parameters used in each iteration of the symmetric successive over-relaxation (SSOR), accelerated over-relaxation (AOR), and symmetric accelerated over-relaxation (SAOR) methods for solving linear equation systems. When the optimal values of the parameters in the SSOR, AOR, and SAOR are hard to determine as some fixed values, they are obtained by minimizing the merit functions, which are based on the maximal projection technique between the left- and right-hand-side vectors, which involves the input vector, the previous step values of the variables, and the parameters. The novelty is a new concept of the dynamical optimal values of the parameters, instead of the fixed values and the maximal projection technique. In a preferred range, the optimal values of the parameters can be quickly determined by using the golden section search algorithm with a loose convergence criterion. Without knowing and having the theoretical optimal values in general, the new methods might provide an alternative and proper choice of the values of the parameters for accelerating the convergence speed. Numerical testings of the linear Poisson equation discretized to a matrix–vector form and a Lyapunov equation form were used to assess the performance of the DOSSOR, DOAOR, and DOSAOR dynamical optimal methods.

Modeling on displacement response and damage mechanism of contact interface during installation for composites sleeved interference joint

Interference-fit has remarkable advantages in improving the load-bearing performance of the structure, but the interface damage caused by interference installation becomes a weakness in the reliable application of composite joints. Therefore, a reliable and effective physically-based numerical model to reveal the displacement response and damage mechanism of contact interface during installation for composites sleeved interference joint was developed by combining the physically-based LaRC05 criterion and the energy-based linear softening law in this paper. The Partition Golden Section Search algorithm was employed to balance the accuracy of damage prediction and computational efficiency. The interference installation simulations with different geometric parameters were carried out and validated by experiments. Results show that the larger the bolt-sleeve interference-fit percentage, the more severe the non-uniform plastic deformation of the sleeve in the installation. Increasing the sleeve thickness can improve the uniformity of radial displacement distribution of the sleeve and alleviate the interface damage, but it cannot eliminate the connection gap. Choosing the appropriate sleeved fastener with taper can effectively avoid the aforementioned gap, improving the uniformity of displacement distribution and even reducing the interface damage.

Processing time reduction for UAV optimal altitude and investigating its effect on flight time and energy consumption

ABSTRACT In this article, the time to calculate the optimal height of the UAV is investigated as an important factor in determining the total flight time, energy consumption and total delay. In particular, in this paper, the calculation of the optimal height of the UAV, reducing the time of calculating the optimal height, reducing the energy consumption, reducing the total flight time and reducing the total delay is done. First, using the average path loss and UAV transmitted power functions, we present the optimal height of the UAV in the form of an optimization problem with a convex altitude range. Then, using the golden section search (GSS) algorithm and based on the condition of the function being unimodal, we calculate the optimization problem and obtain the optimal height value, which is the minimum of the average functions of the path loss and the transmitted power of the UAV. Also, using the convexity principle, we show that the average path loss function is convex in the mentioned interval. Next, using the relationship between the time to calculate the optimal height of the drone and the total flight time, we calculate the amount of energy consumed and the total delay. The simulation results using MATLAB show that the time to calculate the optimal height with the proposed algorithm is much faster than other methods. The time to calculate the optimal height in the proposed method is 0.03 s. The energy consumption using the proposed method is 53 kJ, and the flight time is 37 s, considering the stop on the way, which is the lowest value compared to other methods. Also, the total delay in the proposed method is less than in other methods.

Far-field blast responses of sandwich arbitrary polygonal reinforced plate system

This paper presents a spectral element model for investigating the dynamic response characteristics of the arbitrary polygonal built-up reinforced plate system subjected to far-field blast load. In the researched system, the plate elements are made of sandwich materials with functionally graded carbon nanotube reinforced (FG-CNTRC) panels and three-dimensional graphene foam (3D-GrF) core. The stiffness matrix assembly method is incorporated into the spectral element method (SEM) for establishing the overall dynamic formulas of arbitrary assembled plates. Thereinto, the governing equations of motion of plate elements are derived by the Hamilton's principle based on the simple first-order shear deformation theory (S-FSDT) retaining only four displacement variables, which provides an advantage to maintain interelement continuity conditions completely. After that, the natural frequencies and transient responses of the systems with different built-up forms are solved by introducing a golden section search algorithm and Fourier series expansion of the blast load. The admirable predictive accuracy of the present model is verified by comparing the obtained results and the reference solution from finite element method (FEM). Moreover, the effects of the CNT distribution form, CNT volume fraction, 3D-GrF pore distribution form, 3D-GrF porosity, the thickness ratio of the sandwich panel, TNT mass and explosion radius on the transient vibration properties of the system are revealed through a detailed parametric study.

Pharmacokinetic parameter identification using a meshless method approach for transdermal drug delivery

The Localized Collocation Meshless Method (LCMM) is applied to the solution of a set of partial differential equations governing the diffusive transport of a dermally injected compound as described by the Compartmental Pharmacokinetic (CPK) model. This efficient and accurate numerical technique then provides the framework for the estimation of pharmacokinetic (PK) parameters by the comparison of two models, both containing information derived from experimental results, using the iterative Golden Section search algorithm. This comparison is quantified using a norm between the two solution spaces. While this method does provide an estimate of the effective-diffusion coefficient, it ultimately demonstrates that a simple, free-diffusion model is inadequate for quantifying the spatial and temporal distribution of a dermally-injected compound if elimination effects are not accounted for properly.

A Low-Cost and Accurate Microwave Sensor System for Permittivity Characterization

A novel low-cost microwave sensor system is proposed for accurate sensing of the real relative permittivity of materials under test (MUT). The proposed solution eliminates the need for using advanced measurement devices such as the vector network analyzer (VNA) for sensor characterization. The proposed sensor system is built on a software-defined radio platform. A suitable two-stage frequency estimation approach was developed for estimating the frequency shift of the resonator sensor associated with the real relative permittivity of the MUT. First, the neighborhood of the resonance frequency is obtained utilizing a low-resolution coarse search, followed by a fine search method to accurately estimate the resonance frequency. For the fine search, we modified the AM frequency estimation algorithm and the Golden-Section search algorithm, GS method to suite the proposed sensor system. The performance of the proposed sensor system is validated through simulations and experiments. To demonstrate the feasibility of the concept, experiments were conducted by implementing the solution on a Universal Software Radio Peripheral (USRP) transceiver using a resonator sensor for detecting the binary mixture of water and methanol. The results show that the proposed sensor system achieves measurement accuracy comparable to advanced equipment such as the VNA. Thus, the proposed sensor system could be a low-cost alternative for sensor characterization purposes with accuracy comparable to standard equipment.

Research on the Torque Control Strategy of a Distributed 4WD Electric Vehicle Based on Economy and Stability Control

To improve the comprehensive performance of the distributed wheel-side four-wheel-drive electric bus, the problem of optimal distribution of the driving torque of the four wheel-side motors is studied. Aiming at the poor economy and failure of switching control due to the consideration of both straight and steering conditions, this paper proposes a fuzzy yaw moment control strategy based on the golden section search algorithm. Under full working conditions, according to the efficiency characteristics of the front and rear axle drive motors, the golden section search algorithm is used to determine the best front and rear axle motor torque distribution coefficient K to distribute the front and rear axle motor torques. Given the stability problems existing in the steering conditions, based on the optimal torque distribution of the front and rear axles, fuzzy control is used to calculate the expected yaw moment, and the left and right wheel torques are adjusted in real time. The simulation is carried out through TruckSim and MATLAB/Simulink, and a hardware-in-the-loop platform is built for experimentation under step steering conditions and sine wave steering conditions. The results show that the proposed torque optimal distribution strategy can optimally distribute the torque of the four drive motors through the real-time identification of working conditions. Compared with the four-wheel equal distribution, under two different steering conditions, the torque distribution efficiency of the torque distribution strategy using the golden section search algorithm increased by 4.35% and 3.83%, respectively. The energy utilization rate of the whole vehicle is improved under all of the working conditions. Under steering conditions, compared with the four-wheel equal distribution and the torque distribution strategy using the golden section search algorithm under all of the conditions, the yaw rate deviation and the slip angle deviation can be reduced, and the yaw stability has been improved.

Hybrid solar energy and waste heat driving absorption subcooling supermarket CO2 refrigeration system: Energetic, carbon emission and economic evaluation in China

A novel hybrid solar energy and waste heat driving absorption subcooled carbon dioxide (CO2/R744) booster refrigeration system (SE + WH) is proposed to improve the energy efficiency of the traditional CO2 refrigeration system used in supermarkets. The thermodynamic and energy conversion model of the system is established. Then, the optimization method of the two-dimensional golden section search algorithm is introduced to optimize the system energy efficiency taking the variation of ambient temperature and solar radiation intensity into account. Moreover, considering the maldistribution of solar energy and the influence of meteorological conditions in China, eight typical cities are selected to assess the annual performance factor and life cycle carbon emissions to achieve energy saving and carbon emission potentials. The performance of hybrid solar energy and waste heat driving absorption subcooled CO2 booster refrigeration system is the best with the COP enhanced by 3.05–42.30 % at the solar radiation intensity of 1200 W/m2 and the temperature of 0–35 °C in contrast to the baseline system. In addition, the discharge pressure of the new proposed hybrid system can be reduced by 7.86 % when the ambient temperature is 34 °C. The annual performance factor of the new proposed hybrid system in Haikou can be increased by 14.47 %, and the life cycle carbon emissions are effectively reduced by 39.54 %. The payback period is also reduced by 4.01 % and 3.37 % for Beijing and Shanghai. Consequently, the novel configuration of the hybrid absorption subcooling subsystem is recommended, particular in hot or warm climate areas with rich solar energy.

A surface deformation measurement algorithm for reflector antennas based on complex geometrical optics

AbstractThis paper presents a new method to reveal the relation between the surface deformation and near-field amplitude of a reflector antenna based on complex geometrical optics, which could be used as an efficient way to estimate the antenna surface verified by simulation results. The measurement process based on this method is envisaged to be realized by a single scanning of the near-field amplitude which would overcome many limitations of radio holography and phase retrieval methods such as the frequency and elevation. The largest source of error in the original deformation-amplitude equation (DAE) has been corrected by considering the Gaussian feed as a complex point source. To track the ray trajectory so that the improved DAE could be solved, an iteration method including a golden section search algorithm is designed to make the solution converge. By solving the modified DAE, simulation result shows that a more accurate solution could be obtained, and the antenna surface could be recovered to a root mean square error of under 30 microns.

Jet Engine Optimal Preventive Maintenance Scheduling Using Golden Section Search and Genetic Algorithm

Jet engines are critical assets in aircraft, and their availability is crucial in the modern aircraft industry. Therefore, their maintenance scheduling is one of the major tasks an airline has to make during an engine’s lifetime. A proper engine maintenance schedule can significantly reduce maintenance costs without compromising the aircraft's reliability and safety. Different maintenance scheduling approaches have been used for jet engines, such as corrective, preventive, and predictive maintenance strategies. Regarding the safety demands in aircraft industries, preventive maintenance is a frequent maintenance method for jet engines. However, preventive maintenance schedules are often use fixed maintenance intervals, which is usually suboptimal. This paper focuses on minimizing a jet engine's overall maintenance cost by optimizing its preventive maintenance schedule based on an engine’s comprehensive reliability model. A hierarchical optimization framework including the golden section search and genetic algorithms is applied to find the optimal set of preventive maintenance number and their times and the components to be replaced at those times during the jet engine's overall lifetime. The Monte Carlo simulation is used to estimate the engine’s failure times using their lifetime distributions from the reliability model. The estimated failure times are then used to determine the engine's overall corrective and preventive maintenance costs during its lifetime. Finally, an optimal preventive maintenance schedule is proposed for an RB 211 jet engine using the presented method. In the end, comparing the proposed method's overall maintenance cost with two other maintenance methods demonstrates the proposed schedule's effectiveness. The method presented in this paper is generic, and it can be used for other similar engineering systems.

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

A Global Optimization Algorithm for Unconstrained Non-linear Optimization Problems Using Chaotic Neuron Map and Golden Number

This paper presents aninnovative global multi-variable optimization algorithm using one of the best chaotic sequences, the neuron map, a description of which is also provided in the paper. The algorithm uses neuron map in the first stage to move near the global minimum point, as well as in each iteration of the second stage of local search that is done using the N-dimensional golden section search algorithm. The generation and mapping of the neuron variables to the optimization variables along with the stagewise search for the global minimum is explained conscientiously in the work. Numerical results on some benchmark functions and the comparison with a latest state-of-the-art algorithm ispresented in order to demonstrate the efficiency of the proposed algorithm.

Regional wind power probabilistic forecasting based on an improved kernel density estimation, regular vine copulas, and ensemble learning

Reliable wind energy forecasting is crucial for the stable operation of power grids. This paper proposes a regional wind power probabilistic forecasting model comprising an improved kernel density estimation (IKDE), regular vine copulas, and ensemble learning. The IKDE is firstly used to generate the margin probability density function (PDF) of each wind farm and the KDE bandwidth is optimized via the golden-section search algorithm to obtain the best possible prediction. Then, several dependence structures are formulated by building different regular vine copulas based on multiple criteria, and all the dependence structures work together with marginal PDF to generate respective joint distribution functions. Finally, ensemble learning is applied to combine all the joint distribution functions and establish an ultimate distribution function. Furthermore, a novel multi-distribution mega-trend-diffusion (MD-MTD) with parametric optimization is proposed to improve the prediction when the data are insufficient. The results of comparative evaluations conducted on datasets from eight wind farms indicate that the proposed model outperforms existing models in wind power generation prediction. Specifically, the proposed model can reliably forecast power generation for an entire region for the next 24 h with only three months of historical data. In contrast, most benchmark models require a year of data.