A CONSTRAINED LEAST SQUARE METHOD FOR ESTIMATING A SMOOTH, NONNEGATIVE FORWARD RATE SEQUENCE

2005 ◽  
Vol 08 (07) ◽  
pp. 989-998 ◽  
Author(s):  
HIROSHI KONNO ◽  
SUMITO ITO
Keyword(s):  
Optimization Problem ◽  
Market Price ◽  
Optimal Solution ◽  
Region Of Interest ◽  
Least Square Method ◽  
Least Square ◽  
Smoothness Condition ◽  
Forward Rate ◽  
Programming Algorithms ◽  
Fitting Error

We will develop an efficient method for estimating a smooth nonnegative forward rate sequence using the market price of riskless bonds. This method is an improvement of the classical Carleton–Cooper's method based on standard least square method, which often generates a non-smooth forward rate sequence and hence is not used in practice. The method to be proposed in this paper is intended to resolve this difficulty. We will impose a smoothness condition while maintaining the fitting error within an acceptable level. The resulting optimization problem is shown to be convex in the region of interest. Therefore, we can calculate a globally optimal solution very fast by standard nonlinear programming algorithms. We will demonstrate that this method generates a smooth forward rate sequence at the expense of a very small increase of fitting error.

scholarly journals Algorithmic Study on Position and Movement Method of Badminton Doubles

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Yu Xie ◽  
Xiaodong Xie ◽  
Huan Xia ◽  
Zhe Zhao
Keyword(s):  
Optimal Solution ◽  
Least Square Method ◽  
Standing Position ◽  
Plane Graph ◽  
Least Square ◽  
Optimal Position ◽  
Research Results ◽  
Parametric Functions ◽  
Save Energy ◽  
Left Front

The algorithms used by schedulers depend on the complexity of the schedule and constraints for each problem. The position and movement of badminton players in badminton doubles competition is one of the key factors to improve the athletes’ transition efficiency of offense and defense and the rate of winning matches and to save energy consumption. From the perspective of basic theory, the author conducts research on the position and movement of badminton doubles. Based on the numerical analysis method, the optimal model of standing position and direction composed of 7 nonlinear equations is established. In addition, the final of 10 matches of the super series of the world badminton federation in 2019 was selected as the sample of speed parameters. With the help of MATLAB mathematical analysis software, the numerical model established by the least square method was adopted to optimize the specific standing position and walking model. Ultimately, the optimal solution has been obtained, which can be represented on a plane graph. The optimal position of the attack station should be the blocking area (saddle-shaped area) and the hanging area (circular arc area in the middle). The optimal defensive positioning should be left defensive positioning area (left front triangle area) and right defensive positioning area (right front triangle area), which is consistent with our current experience and research results. The research results use mathematical tools to calculate the accurate optimal position in doubles matches, which has guiding significance to the choice of athletes’ position and walking position in actual combat and can also be used as a reference for training, providing a certain theoretical basis for the standing and walking of badminton doubles confrontation. The data collection and operation methods in this study can provide better calculation materials for artificial intelligence optimization and fuzzy operation of motion displacement, which is of great significance in the field of motion, simulation, and the call of parametric functions.

scholarly journals Cutting Blade Measurement of an Ultrasonic Cutting Machine Using Multi-Step Detection

2019 ◽  
Vol 9 (16) ◽  
pp. 3338 ◽  
Author(s):  
Tae-Gu Kim ◽  
Sheikh Faisal Ahmad ◽  
Byoung-Ju Yun ◽  
Hyun Deok Kim
Keyword(s):  
Rotation Angle ◽  
Detection Method ◽  
Region Of Interest ◽  
Least Square Method ◽  
Thickness Measurement ◽  
Least Square ◽  
Step Detection ◽  
Cutting Machine ◽  
Otsu Method ◽  
Binarization Method

An algorithm for measurement of the cutting blade of the ultrasonic vibration cutting machine used in an automation machine is proposed in this paper. The proposed algorithm, which is based upon a multi-step detection method, is developed for the accurate measurement of the cutting blade by exactly determining its rotation angle, length, and thickness. Instead of the commonly used Otsu method, we propose a new curvature-based adaptive binarization method, which provides more accurate details about the dimensions of the cutting blade. A region of interest containing the cutting blade from the acquired image is first extracted in the multi-step detection method, which is further processed to remove the noise, which increases the measurement reliability. An important feature of the proposed process is the restoration of the cutting blade’s tip data, which used to be lost during the fine noise-filtering process. The rotation angle and length are measured using the minimum rotated rectangle while the line fitting based upon the least square method is applied to increase the reliability of the thickness measurement. Experimental results validate the superiority of the proposed method over the conventional Otsu method.

scholarly journals Computer Mathematical Modeling Based on the Improved Genetic Algorithm and Mobile Computing

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Huixian Wei ◽  
Jia Liu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Mobile Computing ◽  
Optimal Solution ◽  
Least Square Method ◽  
Search Space ◽  
Least Square ◽  
Improved Genetic Algorithm ◽  
Operation Rate ◽  
The Individual

In order to change the problem of data redundancy in a genetic algorithm, this paper proposes a computer mathematical model based on the combination of an improved genetic algorithm and mobile computing. Combined with the least square method, MATLAB software is used to solve the equations, determine the range of parameters, and solve the estimation parameter range and identification problems. The improved genetic algorithm combined with mobile computing and least square method to establish a mathematical model greatly increased the individual search space and increased the operation rate of 90% compared to the basic genetic algorithm or mobile computing. The results show that the improved genetic algorithm and mobile computing have a certain ability to identify the optimal solution and greatly improve the work efficiency.

scholarly journals AVALIAÇÃO DA POTENCIALIDADE DE FUNÇÕES OBJETIVO UTILIZADAS NA IDENTIFICAÇÃO DE FALHAS EM ESTRUTRAS TRELIÇADAS

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Marcus Alexandre Noronha de Brito ◽  
Luiano Mendes Bezerra ◽  
Willian Taylor Matias Silva ◽  
Wellington Andrade da Silva
Keyword(s):  
Structural Damage ◽  
Lattice Structure ◽  
Optimal Solution ◽  
Least Square Method ◽  
Least Square ◽  
Objective Functions ◽  
Residual Function ◽  
Internal Damage ◽  
Damage Location ◽  
Natural Modes

RESUMO: A realização da análise de um conjunto de “Assinaturas Estruturais” ou comumente denominadas como “Funções Objetivo” possibilita o conhecimento de suas respectivas potencialidades ou sensibilidades em identificar falhas ou danos estruturais. Cinco Funções Objetivo são avaliadas neste trabalho compostas por grandezas estáticas, deslocamentos, e dinâmicas, como modos e frequências naturais de vibração, de modo a unir a simplicidade de obtenção dos parâmetros estáticos com a potencialidade das características dinâmicas. Ainda se observa que a otimização destas soluções pela minimização de uma função residual com a aplicação de um processo combinatório, juntamente com o Método dos Mínimos Quadrados – MMQ resulta na localização e quantificação de falhas ou danos internos nas barras de uma estrutura treliçada. Dessa forma, avalia-se a sensibilidade das Funções Objetivo na captura dos danos propostos determinando assim a Função que apresenta a solução ótima para o problema estrutural apresentado de localização de dano possibilitando também a observação das dificuldades encontradas nestes problemas. Dessa forma os resultados expostos evidenciam a capacidade das “Funções Objetivo” estudadas em auxiliar ações de análise de localização de danos estruturais internos, reduzindo a aplicação de métodos como ultrassom a locais mais restritos, caso necessário. ABSTRACT: The analysis of a set of "structural signatures" or also called "Objective Functions" enables the knowledge of their respective capabilities or sensitivities to identify flaws or structural damage. Five objective functions are evaluated in this work comprised of static quantities, offsets and processes as natural modes and frequencies of vibration, so as to combine the simplicity of obtaining static parameters with the capability of dynamic characteristics. Still noted that optimization of these solutions by minimizing a residual function with the application of a combinatorial procedure with the least square method - resulting in MMQ location and quantification of failures or internal damage to the bars of a lattice structure. Thus, it evaluates the sensitivity of the functions goal in the capture of the proposed damage thus determining the function that provides the optimal solution to the problem presented structural damage location also enables the observation of the difficulties encountered these problems. Thus, the results show the ability of the "Objective Functions" studied to assist in the analysis of the location of internal structural damage, reducing the application of methods such as ultrasound to more restricted locations, if necessary.

scholarly journals RESEARCH ON VISUAL NAVIGATION PATH DETECTION METHOD FOR DENSE PLUM GROVE

2021 ◽  
pp. 111-118
Author(s):  
XiaoDan Ren ◽  
Haichao Wang ◽  
Xin Shi
Keyword(s):  
Color Space ◽  
Region Of Interest ◽  
Least Square Method ◽  
Detection Algorithm ◽  
Visual Navigation ◽  
Least Square ◽  
Detection Accuracy ◽  
Navigation Path ◽  
Field Management ◽  
Path Detection

Aiming at the field management of plum grove in Inner Mongolia of China, taking the dense planting plum groves in Bikeqi town of Hohhot City as the research object, this paper proposed a visual navigation path detection algorithm for plum grove. By processing the video image information of plum grove, comparing RGB and HSV color space model, HSV color model was selected to separate the plant and background in V channel. Homomorphic filtering was used to highlight the region of interest in the image, Otsu was selected to segment the image, the intersection of plum trunk and ground was extracted as feature points, and the least square method was used to fit the navigation path. Through the comparative analysis of detection rate under different detection conditions in one day, the verification test of route accuracy was carried out. The experimental results show that: for dense planting plum grove, the average path detection accuracy of the algorithm is 70% and 73.3% under the condition of front light and weak light, respectively. The detection accuracy and real-time meet the requirements of plum grove field management, and the navigation baseline can be generated more accurately, which provides a preliminary basis for the realization of mechanical vision navigation in plum grove field management.

scholarly journals Parameter identification and state-of-charge prediction of decommissioned lithium batteries

2021 ◽  
Vol 267 ◽  
pp. 01017
Author(s):  
Qian Shi ◽  
Junkai Li ◽  
Qi Qin ◽  
Chijian Zhang
Keyword(s):  
Parameter Identification ◽  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Lithium Batteries ◽  
Equivalent Circuit Model ◽  
Optimal Solution ◽  
Least Square Method ◽  
State Of Charge ◽  
Least Square ◽  
Recursive Least Square

Aiming at the problem that different temperatures and working modes affect the parameter identification and state of charge (SOC) estimation of decommissioned lithium batteries, a new method based on the second-order RC equivalent circuit model combined with the recursive least square method (RLS) is proposed to introduce the forgetting factor, and combined with the extended Kalman filter algorithm (EKF) to realize the method of online parameter identification of decommissioned lithium batteries and the optimal estimation of SOC. In order to solve the problem of obtaining the optimal solution of the error covariance matrix and the measurement noise covariance matrix in EKF, the particle swarm optimization algorithm (PSO) is used to optimize online to further improve the SOC prediction accuracy. The results show that the joint optimization algorithm can accurately identify the parameters and SOC values of retired lithium batteries, which is helpful to realize the echelon utilization of retired lithium batteries.

Study on paste pumping characteristics based on double pumps in parallel

2015 ◽  
Vol 12 (3) ◽  
pp. 255-260 ◽  
Author(s):  
Guimei Wang ◽  
Shaohua Jin ◽  
Buqin Zhang ◽  
Fugui Yang ◽  
Xiaoli Ji
Keyword(s):  
Objective Function ◽  
Optimal Solution ◽  
Least Square Method ◽  
Least Square ◽  
Pumping System ◽  
Filling Station ◽  
Unit Energy ◽  
Parallel Forms ◽  
Coal Reserves ◽  
Flow Power

The coal reserves overlain by buildings, water bodies and railways are estimated to be about 14 billion tons in China. Based on the concept of green mining, in order to save the unit energy, Double pumps in parallel forms of pumping are adopted in 0the paste filling of the pumping system. The optimal solution of the objective function could be obtained by taking the unit flow power of the pumping system as the objective function, using the quadratic polynomial by the least square method curve fitting and by the application of MATLAB. Thereby it is possible to reduce power consumption and increase the efficiency of the operating economy in the paste filling station.

Optimization Methods for Spectral Synthesizing of a Tuneable Colour Light Source

2018 ◽  
pp. 99-108
Author(s):  
Nina Carli ◽  
Armin Sperling ◽  
Grega Bizjak
Keyword(s):  
Light Source ◽  
Optimization Problem ◽  
Least Square Method ◽  
Optimization Methods ◽  
Least Square ◽  
Light Sources ◽  
Output Spectrum ◽  
Constrained Problem ◽  
Target Spectrum ◽  
Spectral Distributions

A method for a tuneable colour light source (TCLS) output spectrum synthesizing is described. A TCLS is a multichannel LED light source, which is able to mimic and produce different spectral distributions and can be used for the realization of different spectra, e.g. the spectra of different CIE standard illuminants. The synthesizing of output spectrum is actually an optimization problem of tuning the output spectrum of a TCLS to the target spectrum. It is also a so called constrained problem as output spectrum is produced by adding the weighted spectra of used light sources (e.g. singlecolour LEDs) and due to the fact that there is no “negative light”. Because of that usual optimization methods like least square method cannot be used. A novel synthesizing method based on a constrained optimization process was developed and tested on the laboratory TCLS to be used for calibration purposes. The developed synthesizing method, described in this paper, gives good results but comparison with more simple methods shows that also these can be successfully used.

scholarly journals A Novel WSNs Localization Algorithm Based on Artificial Fish Swarm Algorithm

2016 ◽  
Vol 12 (1) ◽  
pp. 64 ◽  
Author(s):  
Xiaoying Yang ◽  
Wanli Zhang ◽  
Qixiang Song
Keyword(s):  
Optimal Solution ◽  
Least Square Method ◽  
Least Square ◽  
Localization Algorithm ◽  
Node Localization ◽  
Artificial Fish Swarm Algorithm ◽  
Network Cost ◽  
Artificial Fish Swarm ◽  
Unknown Node ◽  
The Cost

In node localization algorithm in Wireless Sensor Networks (WSNs), the least square method is affected by the measurement error, which leads to position error of the unknown node. In order to solve the problem that the error is too high, we propose a novel WSNs localization algorithm based on artificial fish swarm (AFSA). In the proposed algorithm, artificial fish swarm, which has some advantages such as requirements for the initial value and parameter setting is not high, the optimization speed is quick and so on, is introduced in position process. Firstly, the distances between nodes are obtained by using the TDOA algorithm. Then the geometrical position of the unknown nodes is estimated by the artificial fish swarm optimization algorithm. The simulation results show that compared with the least square method, the algorithm proposed in the paper can reduce the computation amount, get the optimal solution quickly and improve the accuracy of the node without increasing the cost and power consumption. Moreover, the number of beacon nodes is relatively small, so the network cost is reduced to a certain extent.

Sign in / Sign up

Export Citation Format

Share Document