scholarly journals Optimal Path Analysis for Solving Nonlinear Equations with Finite Local Error

2022 ◽  
Vol 16 ◽  
pp. 94-104
Author(s):  
Xiaoxiao Ma ◽  
Xiaojuan Chen
Keyword(s):  
Nonlinear Equation ◽  
Path Analysis ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Optimal Path ◽  
Optimal Solution ◽  
Equation System ◽  
Local Error ◽  
Analysis Method ◽  
Long Time

Because the traditional method of solving nonlinear equations takes a long time, an optimal path analysis method for solving nonlinear equations with limited local error is designed. Firstly, according to the finite condition of local error, the optimization objective function of nonlinear equations is established. Secondly, set the constraints of the objective function, solve the optimal solution of the nonlinear equation under the condition of limited local error, and obtain the optimal path of the nonlinear equation system. Finally, experiments show that the optimal path analysis method for solving nonlinear equations with limited local error takes less time than other methods, and can be effectively applied to practice

scholarly journals An Integrated Genetic Algorithm and Homotopy Analysis Method to Solve Nonlinear Equation Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hala A. Omar
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equation ◽  
Homotopy Analysis Method ◽  
Optimal Solution ◽  
Initial Guess ◽  
Analysis Method ◽  
Optimization Task ◽  
Homotopy Analysis ◽  
Newton Homotopy ◽  
Nonlinear Equation Systems

Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined objective function. This paper proposes a new algorithm for solving square and nonsquare nonlinear systems combining the genetic algorithm (GA) and the homotopy analysis method (HAM). First, the GA is applied to find out the solution. If it is realized, the algorithm is terminated at this stage as the target solution is determined. Otherwise, the HAM is initiated based on the GA stage’s computed initial guess and linear operator. Moreover, the GA is utilized to calculate the optimum value of the convergence control parameter (h) algebraically without plotting the h-curves or identifying the valid region. Four test functions are examined in this paper to verify the proposed algorithm’s accuracy and efficiency. The results are compared to the Newton HAM (NHAM) and Newton homotopy differential equation (NHDE). The results corroborated the superiority of the proposed algorithm in solving nonlinear equation systems efficiently.

On Adjustable Planar Four-Bar Motion Generation With Order, Branch and Circuit Defect Rectification

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Qiong Shen ◽  
Wen-Tzong Lee ◽  
Kevin Russell
Keyword(s):  
Nonlinear Equation ◽  
Objective Function ◽  
Inequality Constraints ◽  
Equation System ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Order Branch ◽  
Circuit Defects ◽  
Displacement Model ◽  
Defect Elimination

This work is an incremental extension of adjustable planar four-bar kinematic synthesis theory to consider not only synthesis, but also the elimination of the defects inherent in synthesis. A nonlinear equation system for moving pivot-adjustable planar four-bar motion generation that includes constraints for order defect, branch defect and circuit defect elimination is presented in this work. In the objective function of the equation system, the error between the prescribed and achieved precision positions is minimized. The equation system includes inequality constraints to eliminate order defects and branch defects. The equation system also includes a complete planar four-bar displacement model to eliminate circuit defects.

scholarly journals Solution of series-parallel photovoltaic arrays model using global optimization algorithms

2020 ◽  
Vol 25 (1) ◽  
pp. 14-22
Author(s):  
Juan David Bastidas-Rodriguez ◽  
Jorge Mario Cruz-Duarte ◽  
Carlos Rodrigo Correa-Cely
Keyword(s):  
Global Optimization ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Optimization Problem ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Equation System ◽  
System Of Nonlinear Equations ◽  
Electrical Behavior ◽  
Partial Shading

Models of series-parallel (SP) photovoltaic (PV) arrays focus on the system of nonlinear equations that represents the array’s electrical behavior. The solution of the system of nonlinear equations can be posed as an optimization problem and solved with different methods; however, the models do not formulate the optimization problem and do not evaluate different optimization algorithms for its solution. This paper proposes a solution, using global optimization algorithms, of the mathematical model that describes the electrical behavior of a SP generator, operating under uniform and partial shading conditions. Such a model is constructed by dividing the generator into strings and representing each module in the string with the single-diode model. Consequently, for each string a system of nonlinear equations is build applying the Kirchhoff’s laws, where the unknowns are the modules’ voltages. The solution of the resulting nonlinear equation system is posed as an optimization problem, where the objective function is defined as the sum of the squared of each nonlinear equation. Minimum and maximum values of each voltage are defined from the datasheet information of the modules and bypass diodes. As a demonstrative example, we arbitrarily select two well-known algorithms to solve this problem: Genetic Algorithms and Particle Swarm Optimization. Simulation results show that both algorithms solve the optimization problem and allow the reproduction of the generator’s characteristic curves. Moreover, the results also indicate that the optimization problem is correctly defined, which opens the possibility explore other optimization algorithms to reduce the computation time.

Rancang Bangun Sistem Penerimaan Dan Mutasi Barang Pada PDAM Tirta Kerta Raharja

Sensi Journal ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 236-246
Author(s):  
Ilamsyah Ilamsyah ◽  
Yulianto Yulianto ◽  
Tri Vita Febriani
Keyword(s):  
System Analysis ◽  
Object Oriented ◽  
Analysis Method ◽  
Web Based ◽  
Visual Modeling ◽  
Long Time ◽  
The Right ◽  
And Control ◽  
Web Based System ◽  
The Web

The right and appropriate system of receiving and transferring goods is needed by the company. In the process of receiving and transferring goods from the central warehouse to the branch warehouse at PDAM Tirta Kerta Raharja, Tangerang Regency, which is currently done manually is still ineffective and inaccurate because the Head of Subdivision uses receipt documents, namely PPBP and mutation of goods, namely MPPW in the form of paper as a submission media. The Head of Subdivision enters the data of receipt and mutation of goods manually and requires a relatively long time because at the time of demand for the transfer of goods the Head of Subdivision must check the inventory of goods in the central warehouse first. Therefore, it is necessary to hold a design of information systems for the receipt and transfer of goods from the central warehouse to a web-based branch warehouse that is already database so that it is more effective, efficient and accurate. With the web-based system of receiving and transferring goods that are already datatabed, it can facilitate the Head of Subdivision in inputing data on the receipt and transfer of goods and control of stock inventory so that the Sub Head of Subdivision can do it periodically to make it more effective, efficient and accurate. The method of data collection is done by observing, interviewing and studying literature from various previous studies, while the system analysis method uses the Waterfall method which aims to solve a problem and uses design methods with visual modeling that is object oriented with UML while programming using PHP and MySQL as a database.

scholarly journals Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 260
Author(s):  
Meng Suo ◽  
Dong Zhang ◽  
Yan Yang
Keyword(s):  
Nonlinear Equations ◽  
Waveform Inversion ◽  
Optimal Solution ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Elastic Wave Equation ◽  
Full Waveform ◽  
Ultrasonic Propagation ◽  
Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

2021 ◽  
Author(s):  
José Correa ◽  
Paul Dütting ◽  
Felix Fischer ◽  
Kevin Schewior
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Optimal Solution ◽  
Random Order ◽  
Secretary Problem ◽  
Maximum Value ◽  
Optimal Stopping Theory ◽  
Long Time ◽  
Object Of Study ◽  
Independent And Identically Distributed

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

Enhanced UAS Surveillance Using a Video Utility Metric

2013 ◽  
Vol 01 (02) ◽  
pp. 277-296 ◽  
Author(s):  
Peter C. Niedfeldt ◽  
Brandon T. Carroll ◽  
Joel A. Howard ◽  
Randal W. Beard ◽  
Bryan S. Morse ◽  
...  
Keyword(s):  
Planning Process ◽  
Optimal Path ◽  
Optimal Solution ◽  
Flight Test ◽  
Video Stream ◽  
Flight Path ◽  
Optimal Path Planning ◽  
Planning Approach ◽  
Human Operators ◽  
Imaging Sensors

A successful mission for an Unmanned Air System (UAS) often depends on the ability of human operators to utilize data collected from onboard imaging sensors. Many hours are spent preparing and executing flight objectives, putting a tremendous burden on human operators both before and during the flight. We seek to automate the planning process to reduce the workload for UAS operators while also optimizing the quality of the collected video stream. We first propose a metric based on an existing image utility metric to estimate the utility of video captured by onboard cameras. We then use this metric to not only plan the UAS flight path, but also the path of the camera's optical axis projected along the terrain and the zoom level. Since computing an optimal solution is NP-hard and therefore infeasible, we subsequently describe a staged sub-optimal path planning approach to autonomously plan the UAS flight path and sensor schedule. We apply these algorithms to precompute UAS and sensor paths for a surveillance mission over a specified region. Simulated and actual flight test results are included.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

Sign in / Sign up

Export Citation Format

Share Document