scholarly journals On the Problem of Choosing Optimal Methods for Approximating Functions

2021 ◽  
Vol 2096 (1) ◽  
pp. 012054
Author(s):  
I A Bordanov ◽  
S N Zhiganov ◽  
S N Danilin
Keyword(s):  
Control Systems ◽  
Error Function ◽  
Approximation Error ◽  
Feedforward Neural Networks ◽  
Absolute Error ◽  
Maximum Absolute Error ◽  
Computational Costs ◽  
Root Functions ◽  
The Best Approximation ◽  
Mathematical Operations

Abstract The materials of the article relate to the field of optimization of control systems and signal processing when preparing models for technical implementation. The informational level of structural and functional decomposition of models of approximators of square root functions is considered. The article investigates two classes of computational methods: sequential - polynomials of the best approximation and parallel - multilayer feedforward neural networks. For each of the classes, using particular examples, the approximation error was calculated according to the criteria of the maximum absolute error and the area of the error function, as well as the computational costs as the sum of the number of mathematical operations and queries in the memory of the calculator.

Error Compensation Techniques for Fixed-Width Array Multiplier Design — A Technical Survey

2016 ◽  
Vol 26 (03) ◽  
pp. 1730003 ◽  
Author(s):  
S. Balamurugan ◽  
P. S. Mallick
Keyword(s):  
Error Compensation ◽  
Absolute Error ◽  
Mean Square ◽  
Maximum Absolute Error ◽  
Comprehensive Review ◽  
Related Research ◽  
Error Formula ◽  
Error Metrics ◽  
Array Multiplier ◽  
Future Work

This paper provides a comprehensive review of various error compensation techniques for fixed-width multiplier design along with its applications. In this paper, we have studied different error compensation circuits and their complexities in the fixed-width multipliers. Further, we present the experimental results of error metrics, including normalized maximum absolute error [Formula: see text], normalized mean error [Formula: see text] and normalized mean-square error [Formula: see text] to evaluate the accuracy of fixed-width multipliers. This survey is intended to serve as a suitable guideline and reference for future work in fixed-width multiplier design and its related research.

Spatial Dynamic Analysis of a Mangeove Patch Based on Unmanned Aerial Vehicle: A Case Study in Pear Bay in Guangxi, China

2021 ◽  
Author(s):  
Xin Lin ◽  
Chungan Li ◽  
Mei Zhou ◽  
Wenhai Liang ◽  
Biao Li
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Spatial Dynamics ◽  
Absolute Error ◽  
Maximum Error ◽  
Canopy Height ◽  
Accurate Information ◽  
Maximum Absolute Error ◽  
Patch Area ◽  
Maximum Increase ◽  
Aerial Vehicle

Abstract This study investigated the short-term spatial variability of an mangrove patch, located in the Pearl Bay in Guangxi, China. Unmanned aerial vehicle (UAV) imagery covering the period from March 2015 to October 2017 were used and the following models were developed: two annual ultra-high resolution spatial resolution digital orthophoto maps (DOMs), two digital elevation models (DEMs), two digital surface models (DSMs), two canopy height models (CHMs), and a canopy height difference model (d-CHM). Using these models, the spatial dynamics of the extent and canopy height of the patch were analyzed. The resolution of the DOMs was 0.1 m, with an average geometrical error of 0.17 m and a maximum error of 0.44 m. The resolutions of DEMs, DSMs, CHMs, d-CHM were all 1 m. The average elevation errors of CHM in 2015 and 2017 were 0.002 m and -0.001 m, respectively, with maximum absolute errors of 0.034 m and 0.030 m, respectively. The average elevation error of d-CHM was -0.003 m and the maximum absolute error was 0.036 m, and the data quality were rated as good. From 2015 to 2017, the area of the mangrove patch increased from 8.16 ha to 8.79 ha, with an average annual increase of 3.7%. Specifically, the areas of expansion, shrinkage, and maximum seaward expansion were 6356 m2, 19 m2, and 24 m, respectively. The driving factor for the variability was natural processes. Stand canopy height exhibited a particular trend of decrease from northwest to southeast (horizontal; parallel to the seawall) and from the land to the sea (vertically; perpendicular to the seawall). From 2015 to 2017, 88.2% of the patch area showed increased canopy height, with an average increase of 0.78 m and a maximum increase of 3.2 m. In contrast, 11.8% of the patch area showed decreased canopy height with a maximum decrease of 3.1 m. The main reason for the decrease in canopy height was the death of trees caused by serious insect plagues. On the other hand, the reason for the increase in height could be attributed to the natural growth of mangrove trees, but further studies are required to verify the cause. UAV remote sensing has an incomparable advantage over traditional methods in that it provides extremely detailed and highly accurate information for in-depth study of the spatial evolution of mangrove patches, which would significantly contribute towards the protection and management of mangroves.

A numerical method for the approximation of reachable sets of linear control systems

2017 ◽  
Vol 36 (2) ◽  
pp. 423-441 ◽  
Author(s):  
Lizhen Shao ◽  
Fangyuan Zhao ◽  
Guangda Hu
Keyword(s):  
Numerical Method ◽  
Control Systems ◽  
Optimization Problems ◽  
Approximation Error ◽  
Outer Approximation ◽  
Reachable Sets ◽  
Linear Control ◽  
Superior Performance ◽  
Linear Control Systems ◽  
Inner Approximation

Abstract In this article, a numerical method for the approximation of reachable sets of linear control systems is discussed. First a continuous system is transformed into a discrete one with Runge–Kutta methods. Then based on Benson’s outer approximation algorithm for solving multiobjective optimization problems, we propose a variant of Benson’s algorithm to sandwich the reachable set of the discrete system with an inner approximation and an outer approximation. By specifying an approximation error, the quality of the approximations measured in Hausdorff distance can be directly controlled. Furthermore, we use an illustrative example to demonstrate the working of the algorithm. Finally, computational experiments illustrate the superior performance of our proposed algorithm compared to a recent algorithm in the literature.

scholarly journals Method of Measuring Liquid Water Mass Fraction of Snow by Alcohol Solution

1986 ◽  
Vol 32 (112) ◽  
pp. 538-539 ◽  
Author(s):  
D. Fisk
Keyword(s):  
Liquid Water ◽  
Water Mass ◽  
Field Measurements ◽  
Absolute Error ◽  
Liquid Water Content ◽  
Snow Sample ◽  
Maximum Absolute Error ◽  
Water Fraction ◽  
Single Operator ◽  
Temperature Depression

Abstracta method of making field measurements of the liquid water fraction of snow has been developed in which a snow sample is dissolved in methanol to produce a temperature depression. The depression is linearly related to the liquid water content of the snow sample. a single operator can perform four to five measurements per hour with a maximum absolute error of 1.0%.

Prediction Model of Micum Strength for Iron Ore Sinter

2011 ◽  
Vol 402 ◽  
pp. 476-479
Author(s):  
Wei Wang ◽  
Zhi Hui Xu ◽  
Long Long Yang ◽  
Zheng Liang Xue ◽  
Dong Nan Zhao ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Absolute Error ◽  
Maximum Absolute Error ◽  
Important Indicator ◽  
The Neural Network ◽  
Iron Ore Sinter ◽  
Real Value ◽  
The Law

Micum strength is an important indicator of quality of sinter; BP artificial neural network model is built to predict the strength of sinter drum. The neural network use the main factors that influence the sinter drum as input data, and output is Micum strength. Experiment results shows that the maximum absolute error between the Micum strength predicted by neural network and real value from the sinter plant is 0.3346, and the average absolute error is 0.1154. These prove that the prediction is accuracy. In addition, because of the "black box" characteristic of the neural network model, the neural network model can not give the law of how the various factors affect the micum strength of sinter ore, this paper also uses the model to analysis the law of how TFe, SiO2 content affect the micum strength. The results not only consist with the sintering theory, but also verify the validity of the model.

Dynamic Finite Element Analysis and Experimental Study of Rotating Column in Cylinder

2012 ◽  
Vol 229-231 ◽  
pp. 453-456
Author(s):  
Zhi Miao Li ◽  
Ju Bao Liu ◽  
Min Luo ◽  
Qiang Zhang
Keyword(s):  
Experimental Study ◽  
Outer Cylinder ◽  
Absolute Error ◽  
Coupling Model ◽  
Contact Forces ◽  
Transverse Displacement ◽  
Maximum Absolute Error ◽  
Element Analysis ◽  
Axial Acceleration ◽  
Slender Column

Rotary slender column in cylinder is a special structure in oil engineering. It contacts with outer cylinder and interacts with its inner pipe fluid and outer annular fluid. A partitioned coupling model was founded by dispersing slender column into beam element, dividing fluid domain into some sections, dispersing fluid section into hexahedron unit and transfer method of the information of coupling interface was described. Dynamics experimental device of column-liquid interaction was built to do column rotating test with considering the displacement and force boundary conditions of rotating column and testing axial excitation force of bottom column, axial acceleration of head column, transverse displacement of columns and collision and contact forces between inner columns and outer pipeline. The maximum absolute error between experimental results and numerical results is 0.31mm and this research provides the methods of numerical simulation and experimental study.

Validation of Adaptive Gaussian Process Regression Model Used for SIF Prediction

2018 ◽  
Author(s):  
Arvind Keprate ◽  
R. M. Chandima Ratnayake ◽  
Shankar Sankararaman
Keyword(s):  
Regression Model ◽  
Gaussian Process ◽  
Prediction Accuracy ◽  
Experimental Validation ◽  
Gaussian Process Regression ◽  
Absolute Error ◽  
Coefficient Of Determination ◽  
Data Sets ◽  
Maximum Absolute Error ◽  
Data Points

The main aim of this paper is to perform the validation of the adaptive Gaussian process regression model (AGPRM) developed by the authors for the Stress Intensity Factor (SIF) prediction of a crack propagating in topside piping. For validation purposes, the values of SIF obtained from experiments available in the literature are used. Sixty-six data points (consisting of L, a, c and SIF values obtained by experiments) are used to train the AGPRM, while four independent data sets are used for validation purposes. The experimental validation of the AGPRM also consists of the comparison of the prediction accuracy of AGPRM and Finite Element Method (FEM) relative to the experimentally derived SIF values. Four metrics, namely, Root Mean Square Error (RMSE), Average Absolute Error (AAE), Maximum Absolute Error (MAE), and Coefficient of Determination (R2), are used to compare the accuracy. A case study illustrating the development and experimental validation of the AGPRM is presented. Results indicate that the prediction accuracy of the AGPRM is comparable with and even higher than that of the FEM, provided the training points of the AGPRM are aptly chosen.

scholarly journals Intelligent Calibration of a Heavy-Duty Mechanical Arm in Coal Mine

Electronics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1186
Author(s):  
Yunhong Jia ◽  
Xiaodong Zhang ◽  
Zhenchong Wang ◽  
Wei Wang
Keyword(s):  
Extreme Learning Machine ◽  
Coal Mine ◽  
Absolute Error ◽  
Calibration Method ◽  
Heavy Duty ◽  
Maximum Absolute Error ◽  
Positioning Accuracy ◽  
Positioning Errors ◽  
Roof Bolter ◽  
Learning Machine

Accurate positioning of an airborne heavy-duty mechanical arm in coal mine, such as a roof bolter, is important for the efficiency and safety of coal mining. Its positioning accuracy is affected not only by geometric errors but also by nongeometric errors such as link and joint compliance. In this paper, a novel calibration method based on error limited genetic algorithm (ELGA) and regularized extreme learning machine (RELM) is proposed to improve the positioning accuracy of a roof bolter. To achieve the improvement, the ELGA is firstly implemented to identify the geometric parameters of the roof bolter’s kinematics model. Then, the residual positioning errors caused by nongeometric facts are compensated with the regularized extreme learning machine (RELM) network. Experiments were carried out to validate the proposed calibration method. The experimental results show that the root mean square error (RMSE) and the mean absolute error (MAE) between the actual mast end position and the nominal mast end position are reduced by more than 78.23%. It also shows the maximum absolute error (MAXE) between the actual mast end position and the nominal mast end position is reduced by more than 58.72% in the three directions of Cartesian coordinate system.

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