Golden Section Search Research Articles

PEMILIHAN PARAMETER OPTIMUM MENGGUNAKAN EXPONENTIAL SMOOTHING DENGAN METODE GOLDEN SECTION UNTUK PERAMALAN JUMLAH TITIK PANAS DI KALIMANTAN TIMUR

The exponential smoothing method is one method that can be used to predict time series data by smoothing the data. In this study, the method used was exponential smoothing with one smoothing parameter from Brown. The data used is the number of hotspots in East Kalimantan from January 2019 to September 2019. The purpose of this study is to obtain the optimum smoothing parameter values for exponential smoothing from the results of the optimization process using the golden section method to minimize the MAPE value, to obtain forecasting results for each method in exponential smoothing for the number of hotspots in East Kalimantan from October to December 2019, and obtain a good exponential smoothing method to predict data on the number of hotspots in East Kalimantan. From this analysis, the researchers chose the methods used were DES and TES. The optimum smoothing parameter obtained at DES was 0,558430 and TES was 0,376352. The results of forecasting the number of hotspots obtained in DES in October were 2.142, November was 2.707, and December was 3.271 with a MAPE value of 95%. The TES method forecasting results were obtained in October as many as 2.193, November as much as 2.975, and December as many as 3.852 with a MAPE value of 108%. Based on the comparison of the MAPE values in the two methods, the DES method is better than the TES for calculating the predicted value of the number of hotspots in East Kalimantan, although the two methods are not yet suitable for handling this case.

An Orthopedic Auxiliary Diagnosis System Based on Image Recognition Technology.

There are many kinds of orthopedic diseases with complex professional background, and it is easy to miss diagnosis and misdiagnosis. The computer-aided diagnosis system of orthopedic diseases based on the key technology of medical image processing can locate and display the lesion location area by visualization, measuring and providing disease diagnosis indexes. It is of great significance to assist orthopedic doctors to diagnose orthopedic diseases from the perspective of visual vision and quantitative indicators, which can improve the diagnosis rate and accuracy of orthopedic diseases, reduce the pain of patients, and shorten the treatment time of diseases. To solve the problem of possible spatial inconsistency of medical images of orthopedic diseases, we propose an image registration method based on volume feature point selection and Powell. Through the linear search strategy of golden section method and Powell algorithm optimization, the best spatial transformation parameters are found, which maximizes the normalized mutual information between images to be registered, thus ensuring the consistency of two-dimensional spatial positions. According to the proposed algorithm, a computer-aided diagnosis system of orthopedic diseases is developed and designed independently. The system consists of five modules, which can complete many functions such as medical image input and output, algorithm processing, and effect display. The experimental results show that the system developed in this paper has good results in cartilage tissue segmentation, bone and urate agglomeration segmentation, urate agglomeration artifact removal, two-dimensional and three-dimensional image registration, and visualization. The system can be applied to clinical gout and cartilage defect diagnosis and evaluation, providing sufficient basis to assist doctors in making diagnosis decisions.

Research on machining parameter optimization in finishing milling with multiple constraints

High efficiency and high precision milling, as the eternal goal of CNC machining, needs to balance many constraints for selecting the most reasonable processing parameters. This paper presents an efficient machining parameter optimization method for finishing milling operation with multiple constraints. Firstly, under the multiple constraints of parameter feasible region, milling force, milling stability, roughness, and machining contour accuracy, a multi-variable parameter optimization model with machining efficiency as the objective is established. A four level cycle optimization strategy has been detailly described for solving the optimization problem, in which the feed per tooth is optimized by using the golden section method, and with the aid of the random vector search method, the spindle speed, radial, and axial depth cuts are both numerically iterated. The optimal machining parameter combination of the tooth number, feed per tooth, spindle speed, radial, and axial depth of cuts are achieved at last. Finally, the experimental verification results show that the proposed method can greatly improve the machining efficiency under chatter free condition and achieve an efficient finishing milling with consideration of the multiple constraints.

New One-Dimensional Search Iteration Algorithm and Engineering Application

In structural optimization design, obtaining the optimal solution of the objective function is the key to optimal design, and one-dimensional search is one of the important methods for function optimization. The Golden Section method is the main method of one-dimensional search, which has better convergence and stability. Based on the solution of the Golden Section method, this paper proposes an efficient one-dimensional search algorithm, which has the advantages of fast convergence and good stability. An objective function calculation formula is introduced to compare and analyse this method with the Golden Section method, Newton method, and Fibonacci method. It is concluded that when the accuracy is set to 0.1, the new algorithm needs 3 iterations to obtain the target value. The Golden Section method takes 11 iterations, and the Fibonacci method requires 11 iterations. The Newton method cannot obtain the target value. When the accuracy is set to 0.01, the number of iterations of the new method is still the least. The optimized design of the T-section beam is introduced for engineering application research. When the accuracy is set to 0.1, the new method needs 3 iterations to obtain the target value and the Golden Section method requires 13 iterations. When the accuracy is set to 0.01, the new method requires 4 iterations and the Golden Section method requires 18 iterations. The new method has significant advantages in the one-dimensional search optimization problem.

Regret in the Newsvendor Model with Demand and Yield Randomness

We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data‐driven distributionally robust optimization approach to hedge against all distributions that are sufficiently close to a uniform and discrete distribution of empirical data, where closeness is measured by the type‐∞ Wasserstein distance. We adopt the minimax regret decision criterion to assess the optimal order quantity that minimizes the worst‐case regret. Several properties about the minimax regret model, including optimality condition, regret bound, and the worst‐case distribution, are presented. The optimal order quantity can be determined via an efficient golden section search. We extend the analysis to the Hurwicz criterion model, which generalizes the popular albeit pessimistic maximin model (maximizing the worst‐case expected profit) and its (less noticeable) more optimistic counterpart—the maximax model (maximizing the best‐case expected profit). Finally, we present numerical comparisons of our data‐driven minimax regret model with data‐driven models based on the Hurwicz criterion and with a minimax regret model based on partial statistical information on moments.

Research on Joint-Angle Prediction Based on Artificial Neural Network for Above-Knee Amputees.

In the current study, our research group proposed an asymmetric lower extremity exoskeleton to enable above-knee amputees to walk with a load. Due to the absence of shank and foot, the knee and ankle joint at the amputation side of the exoskeleton lack tracking targets, so it is difficult to realize the function of assisted walking when going up and downstairs. Currently, the use of lower-limb electromyography to predict the angles of lower limb joints has achieved remarkable results. However, the prediction effect was poor when only using electromyography from the thigh. Therefore, this paper introduces hip-angle and plantar pressure signals for improving prediction effect and puts forward a joint prediction method of knee- and ankle-joint angles by electromyography of the thigh, hip-joint angle, and plantar pressure signals. The generalized regression neural network optimized by the golden section method is used to predict the joint angles. Finally, the parameters (the maximum error, the Root-Mean-Square error (RMSE), and correlation coefficient ()) were calculated to verify the feasibility of the prediction method.

Power and Rate Adaptive Pushing Over Fading Channels

Proactive caching is capable of reducing access latency and improving network throughput, thereby attracting attention from both industry and academia. However, the energy efficiency (EE) of proactive caching over fading channels has not been well studied yet. In this paper, we aim at presenting an energy-efficient content pushing policy by carefully adapting the transmit rate and power in pushing and on-demand delivery phases, while assuring delivery delay constraints. To this end, the average delay, delay-outage probability, and EE are analyzed for a general adaptive pushing policy based on the saddle point approximation. According to these results, we formulate EE maximization problems under average delay and delay-outage constraints, respectively, for two special types of adaptive pushing policies, namely, opportunistic pushing and water-filling-based pushing. Due to the high complexity of the grid search for solving the formulated problems, suboptimal algorithms are presented based on gradient descent and golden section search methods. Moreover, we mathematically derive the scaling property and numerically obtain request probability and delivery delay thresholds for content pushing. Simulations show that the presented pushing policies achieve higher EE than on-demand transmissions, especially when the content item is popular and the tolerable delivery delay is small.

Про пришвидшення оптимізаційних методів для задачі синтезу багатошарових оптичних покриттів

Розглянуто п’ять способів для пришвидшення багатовимірного пошуку розв’язку задачі синтезу багатошарових оптичних покриттів за допомогою методів нульового та першого порядків. Перший спосіб — це використання аналітичної похідної для цільової функції якості багатошарового покриття. Він дозволяє точно (у межах комп’ютерної арифметики) обчислити значення градієнта гладкої цільової функції та узагальненого градієнта негладкої цільової функції. Перший спосіб потребує таку ж кількість арифметичних операцій, як і скінченно-різницеві способи обчислення градієнта та узагальненого градієнта. Другий спосіб — це використання пришвидшеного знаходження градієнта цільової функції за допомогою використання префікс- та суфікс-масивів у аналітичному способі обчислення градієнта. Цей прийом дозволяє зменшити кількість арифметичних операцій втричі для задач великої розмірності. Третій спосіб — це використання табуляції значень тригонометричних функцій для обчислення характеристичних матриць. Цей прийом зменшує час виконання операцій множення характеристичних матриць у десятки разів в залежності від характеристик комп’ютера. Для деяких архітектур комп’ютера ця перевага становить більше ніж 140 разів. Четвертий спосіб — це використання методу золотого перерізу для одновимірної оптимізації в задачах синтезу оптичних покриттів. Зокрема, при розв’язанні однієї часткової задачі показано, що метод тернарного пошуку потребує приблизно на 40 % більше часових затрат, ніж метод золотого перерізу. П’ятий спосіб — це використання ефективної реалізації множення двох матриць. Вона полягає у зміні порядку другого і третього циклів для загальновідомого методу множення двох матриць та фіксації у звичайній змінній значення елемента першої матриці. Це дозволяє суттєво прискорити виконання операції множення двох матриць. Для матриць розмірності 1000×1000 придшвидшення складає від 2 до 15 разів — залежно від характеристик комп’ютера.

A comprehensive implicit substepping integration scheme for multisurface plasticity

AbstractA complex elastoplastic model requires a robust integration procedure of the evolution equations. The performance of the finite element solution is directly affected by the convergence characteristics of the state‐update procedure. Thereby, this study proposes a comprehensive numerical integration scheme to deal with generic multisurface plasticity models. This algorithm is based on the backward Euler method aiming at accuracy and stability, and on the Newton–Raphson method to solve the unconstrained optimization problem. In this scenario, a line search strategy is adopted to improve the convergence characteristics of the algorithm. The golden section method, an exact line search, is considered. Also, a substepping scheme is implemented to provide additional robustness to the state‐update procedure. Therefore, this work contributes to computational plasticity presenting an adaptive substep size scheme and a consistent tangent modulus according to the substepping technique. Finally, some numerical problems are evaluated using the proposed algorithm. Single‐surface and novel multisurface plasticity models are employed in these analyses. The results testify how the line search and substepping strategies can improve the robustness of the nonlinear analysis.

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.

A Markovian approach to modeling a periodic order‐up‐to‐level policy under stochastic discrete demand and lead time with lost sales

AbstractIn this paper, a periodic order‐up‐to‐level policy is developed by using a Markovian approach. Customer demand is modeled by using an empirical distribution. Unmet customer demand is considered as lost sales. The internal storage capacity is limited, and excessive units are stored in external storage space. Replenishment lead time is discrete and stochastic. Because of the characteristics of the demand and lead time, the demand during the lead time and the demand during the protection interval are empirical. The Markovian approach is used to estimate the system measures of performance, including the expected inventory on‐hand, expected lost sales, and expected over‐storage. The successive overrelaxation algorithm is implemented to overcome the dimensional issue of the Markov model. The optimal policy that minimizes the total cost is obtained by using a customized golden section search procedure. The proposed method is applied to a real dataset of consumable products. In addition, the effectiveness of the approach is demonstrated by a comparison with a simulation. The results indicate that the model from our approach can accurately describe the behavior of the periodic order‐up‐to‐level review system.

Comprehensive evaluation of loess collapsibility of oil and gas pipeline based on cloud theory

The comprehensive evaluation of pipeline loess collapsibility risk is a necessary means to control the safety risks of pipelines in the collapsible loess section. It is also one of the critical scientific bases for risk prevention, control, and management. The comprehensive evaluation system of cloud theory consists of quantitative and qualitative indexes, and the evaluation system has the characteristics of randomness and fuzziness. In view of this problem, the standard qualitative and semi-quantitative evaluation methods have intense subjectivity in dealing with the uncertainty problems such as randomness and fuzziness of the system, the cloud theory, which can effectively reflect the randomness and fuzziness of things at the same time, is introduced. The state scale cloud and index importance weight cloud of pipeline loess collapse risk are constructed by the golden section method. The uncertainty cloud reasoning process of the quantitative indexes and the expert scoring method of the qualitative indexes are proposed. The comprehensive evaluation model of loess collapsibility risk of oil and gas pipeline is established, and the engineering example is analyzed. The complete evaluation results of 10 samples to be evaluated are consistent with the results of the semi-quantitative method and are compatible with the actual situation. The evaluation process softens the subjective division of index boundary, simplifies the preprocessing of index data, realizes the organic integration of quantitative and qualitative decisions, and improves the accuracy, rationality, and visualization of the results.

Perancangan Aplikasi Peramalan untuk Metode Exponential Smoothing Menggunakan Aplikasi Lazarus (Studi Kasus: Data Konsumsi Listrik Kota Samarinda)

Exponential smoothing is forecasting method used to predict the future. Lazarus is an open source software based on free pascal compiler. at this research, program Lazarus be design used exponential smoothing method to predict electricity consumption data in Samarinda City from September to November 2018. Purposed of this researched is to determine the procedure of building an exponential smoothing forecasting application and obtained forecasting result using the built application. Procedure of built the application are designed interface, designed properties and filled coding. The optimum smoothing parameters were obtained used the golden section method. Based on the analysis, electricity consumption data in Samarinda City shows a trend pattern, then the forecasting was used double exponential smoohting (DES) method are DES Brown and DES Holt. The best forecasting method for at this researched is DES Holt, because DES Holt method produced MAPE 0,0659% less than DES Brown method produced MAPE 0,0843%.

Application of edge computing and cloud service data system for doctors' psychological reconstruction after the epidemic

In response to the problems that the new crown pneumonia epidemic may bring to doctors in schools of Chinese medicine, such as information overload, traumatic stress, changes in mentality, crisis of trust, safety when going abroad, and employment choices, explain from the perspective of medical teachers in Chinese medicine schools. The understanding of the epidemic and the major events during the epidemic, combined with the experience of the psychological impact of the past epidemic on the doctors in the school, to highlight the outstanding contributions of medical staff in the fight against the epidemic, and to emphasize the strong leadership of the party and the unity of the people during the fight against the epidemic. The huge role played by Chinese medicine in the fight against the epidemic is the principle. In recent years, cloud computing technology has been continuously developed and improved. Traditional infrastructure as a service has been unable to meet users' needs for cloud computing delivery capabilities. They hope that more and more traditional IT software will be delivered in the form of cloud services. This paper mainly studies the utility optimization and stable matching strategy of UDRN based on EH and limited character input, divides the nodes into multiple clusters, and implements the utility optimization strategy within the clusters. Model users and relays as energy buyers and energy sellers. First, when users choose relays as their candidates, the golden section method is used to obtain the best relay power to maximize user utility. Secondly, based on the principle of maximizing the utility of matching, a mutual preference matrix between users and relays is established. Finally, based on the mutual preference matrix, an improved UDRN stable matching algorithm is proposed through the less complex GS algorithm. This algorithm will play a great role in the psychological reconstruction of doctors after the epidemic.

Self-adaptive bandwidth eigenvector spatial filtering model for estimating PM2.5 concentrations in the Yangtze River Delta region of China.

PM2.5 concentrations are commonly estimated using geographically weighted regression (GWR) models, but these models may suffer from multi-collinearity and over-focus on local feature problems. To overcome these shortcomings, a self-adaptive bandwidth eigenvector spatial filtering (SA-ESF) model utilizing the golden section search (GO-ESF) and genetic algorithm (GA-ESF) was proposed. The SA-ESF model was applied to estimate ground PM2.5 concentrations in the Yangtze River Delta (YRD) region of China both seasonally and annually from December 2015 to November 2016 using remotely sensing data, factory locations, and road networks. The results of the original eigenvector spatial filtering (ESF), GO-ESF, GA-ESF, and GWR models show that the GA-ESF model offers better performance and exhibits a better average adjusted R2 which is 26.6%, 15.3%, and 10.8% higher than for the ESF, GO-ESF, and GWR models, respectively. We next calculated stochastic site indicators that can describe characteristics of regional concentration from interpolated concentration maps derived from the GA-ESF and GWR models. The concentration maps and stochastic site indicators point to major differences in the PM2.5 concentrations in mountainous areas. There are notably high concentrations in those areas using the GWR model, in contrast with the GA-ESF results, indicating that there may be overfitting problems using the GWR model. Overall, the proposed SA-ESF model with the genetic algorithm technique can capture both global and local features and achieve promising results.

FPGA-Based Implementation of an Optimization Algorithm to Maximize the Productivity of a Microbial Electrolysis Cell

In this work, the design of the hardware architecture to implement an algorithm for optimizing the Hydrogen Productivity Rate (HPR) in a Microbial Electrolysis Cell (MEC) is presented. The HPR in the MEC is maximized by the golden section search algorithm in conjunction with a super-twisting controller. The development of the digital architecture in the implementation step of the optimization algorithm was developed in the Very High Description Language (VHDL) and synthesized in a Field Programmable Gate Array (FPGA). Numerical simulations demonstrated the feasibility of the proposed optimization strategy embedded in an FPGA Cyclone II. Results showed that only 21% of the total logic elements, 5.19% of dedicated logic registers, and 64% of the total eight-bits multipliers of the FPGA were used. On the other hand, the estimated power consumption required by the FPGA-embedded optimization algorithm was only 146 mW.

Quantification of thermal energy generation in annular hyperbolic porous-finned heat sinks using inverse optimization

The present paper introduces an accurate numerical procedure to assess the internal thermal energy generation in an annular porous-finned heat sink from the sole assessment of surface temperature profile using the golden section search technique. All possible heat transfer modes and temperature dependence of all thermal parameters are accounted for in the present nonlinear model. At first, the direct problem is numerically solved using the Runge–Kutta method, whereas for predicting the prevailing heat generation within a given generalized fin domain an inverse method is used with the aid of the golden section search technique. After simplifications, the proposed scheme is credibly verified with other methodologies reported in the existing literature. Numerical predictions are performed under different levels of Gaussian noise from which accurate reconstructions are observed for measurement error up to 20%. The sensitivity study deciphers that the surface temperature field in itself is a strong function of the surface porosity, and the same is controlled through a joint trade-off among heat generation and other thermo-geometrical parameters. The present results acquired from the golden section search technique-assisted inverse method are proposed to be suitable for designing effective and robust porous fin heat sinks in order to deliver safe and enhanced heat transfer along with significant weight reduction with respect to the conventionally used systems. The present inverse estimation technique is proposed to be robust as it can be easily tailored to analyse all possible geometries manufactured from any material in a more accurate manner by taking into account all feasible heat transfer modes.

A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

An improved fatigue damage model based on the virtual load spectrum of golden section method

AbstractThis paper presents an improved damage model based on the construction technology of nonlinear partition virtual load spectrum by golden section method which is closer to the actual condition. In contrast to the Palmgren–Miner classical model, the result of fatigue life is more accurate. The improved damage model uses reliability instead of cumulative fatigue damage as the fatigue failure criterion. The objectives in this paper include verifying the convergence of the improved model and analyzing the influence of key parameters on fatigue life. The correction coefficient of the key parameters outperforms the traditional model which ignores the effect of stress sequence on fatigue. The fatigue life of several typical models and improved model is calculated and compared with the experimental results. It is shown that the improved model has higher accuracy and safety.

An Optimization-Based Initial Position Estimation Method for Switched Reluctance Machines

A new method to detect the initial rotor position of switched reluctance machine (SRM) is presented in this article. Unlike most conventional position estimation methods, the proposed method does not need any extra premeasurement and only the data with finite element method (FEM) are required. First, a linear regression model (LRM) is presented to describe the relationship between FEM and measured inductance characteristics. Then, to detect the position, the residual sum of squares of the proposed LRM is considered as an objective function, which is a convex function with rotor position. The rotor position can be estimated by minimizing the objective function with the golden-section search method. Finally, the accuracy of the proposed estimation algorithm is validated by the experimental results on a three-phase 12/8 pole SRM prototype. Compared with the existing position estimation methods, the proposed method has higher accuracy and less measurement effort. The proposed method can serve as a supplement to provide accurate initial position information for incremental position sensors.