UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL

2021 ◽  
pp. 1-43
Author(s):  
Yanqin Fan ◽  
Xuetao Shi
Keyword(s):  
Interval Arithmetic ◽  
Inequality Constraints ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Linear Inequality Constraints ◽  
Linear Equality Constraints ◽  
Linear Equality ◽  
Random Intervals ◽  
Interval Valued

Via generalized interval arithmetic, we propose a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals, where parameters in the model satisfy linear inequality constraints. We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fernández (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.

Analysis of reachable workspace for spatial 3-cable under-constrained suspended cable driven parallel robots

2021 ◽  
pp. 1-42
Author(s):  
Yijia Peng ◽  
Wanghui Bu
Keyword(s):  
Linear Equations ◽  
Inequality Constraints ◽  
Parallel Robots ◽  
The Novel ◽  
Linear Inequality Constraints ◽  
Reachable Workspace ◽  
Linear Equality Constraints ◽  
Equilateral Triangles ◽  
Anchor Points ◽  
Branch And Prune

Abstract Workspace is an important reference for design of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literatures study the workspace of under-constrained CDPRs. In this paper, the static equilibrium reachable workspace (SERW) of spatial 3-cable under-constrained CDPRs is solved numerically since expressions describing workspace boundaries cannot be obtained in closed form. The analysis steps to solve the SERW are as follows. First, expressions which describe the SERW and its boundaries are proposed. Next, these expressions are instantiated through the novel anchor points model composed of linear equations, quadratic equations and limits of tension in cables. Then, based on the reformulated linearization technique (RLT), the constraint system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by 2 examples. One is a special 3-cable CDPR in which the anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by the method to extract the SERW boundary where cables do not interfere with each other. The other is a general case with randomly selected geometry arrangement. The presented method in this paper is universal for spatial 3-cable CDPRs with arbitrary geometry parameters.

Linear Regression Models for Interval-Valued Data using Log-transformation

2020 ◽  
Author(s):  
Nykolas Mayko Maia Barbosa ◽  
João Paulo Pordeus Gomes ◽  
César Lincoln Cavalcante Mattos ◽  
Diêgo Farias Oliveira
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Log Transformation ◽  
Interval Valued

Optimum Path Planning for Mechanical Manipulators

1981 ◽  
Vol 103 (2) ◽  
pp. 142-151 ◽  
Author(s):  
J. Y. S. Luh ◽  
C. S. Lin
Keyword(s):  
Path Planning ◽  
Feasible Solution ◽  
Computing Time ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Linear Inequality Constraints ◽  
Nonlinear Inequality ◽  
Angular Velocities ◽  
Nonlinear Inequality Constraints

To assure a successful completion of an assigned task without interruption, such as the collision with fixtures, the hand of a mechanical manipulator often travels along a preplanned path. An advantage of requiring the path to be composed of straight-line segments in Cartesian coordinates is to provide a capability for controlled interaction with objects on a moving conveyor. This paper presents a method of obtaining a time schedule of velocities and accelerations along the path that the manipulator may adopt to obtain a minimum traveling time, under the constraints of composite Cartesian limit on linear and angular velocities and accelerations. Because of the involvement of a linear performance index and a large number of nonlinear inequality constraints, which are generated from physical limitations, the “method of approximate programming (MAP)” is applied. Depending on the initial choice of a feasible solution, the iterated feasible solution, however, does not converge to the optimum feasible point, but is often entrapped at some other point of the boundary of the constraint set. To overcome the obstacle, MAP is modified so that the feasible solution of each of the iterated linear programming problems is shifted to the boundaries corresponding to the original, linear inequality constraints. To reduce the computing time, a “direct approximate programming algorithm (DAPA)” is developed, implemented and shown to converge to optimum feasible solution for the path planning problem. Programs in FORTRAN language have been written for both the modified MAP and DAPA, and are illustrated by a numerical example for the purpose of comparison.

scholarly journals Non-Linear Regression Models with Vibration Amplitude Optimization Algorithms in a Microturbine

Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 130
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
L. A. Montoya-Santiyanes ◽  
José Manuel Álvarez-Alvarado
Keyword(s):  
Linear Regression ◽  
Vibration Amplitude ◽  
Regression Models ◽  
Engineering Problem ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Gray Wolf ◽  
Linear Regression Models ◽  
Machinery Condition Monitoring ◽  
Non Linear

Machinery condition monitoring and failure analysis is an engineering problem to pay attention to among all those being studied. Excessive vibration in a rotating system can damage the system and cannot be ignored. One option to prevent vibrations in a system is through preparation for them with a model. The accuracy of the model depends mainly on the type of model and the fitting that is attained. The non-linear model parameters can be complex to fit. Therefore, artificial intelligence is an option for performing this tuning. Within evolutionary computation, there are many optimization and tuning algorithms, the best known being genetic algorithms, but they contain many specific parameters. That is why algorithms such as the gray wolf optimizer (GWO) are alternatives for this tuning. There is a small number of mechanical applications in which the GWO algorithm has been implemented. Therefore, the GWO algorithm was used to fit non-linear regression models for vibration amplitude measurements in the radial direction in relation to the rotational frequency in a gas microturbine without considering temperature effects. RMSE and R2 were used as evaluation criteria. The results showed good agreement concerning the statistical analysis. The 2nd and 4th-order models, and the Gaussian and sinusoidal models, improved the fit. All models evaluated predicted the data with a high coefficient of determination (85–93%); the RMSE was between 0.19 and 0.22 for the worst proposed model. The proposed methodology can be used to optimize the estimated models with statistical tools.

scholarly journals Customer Satisfaction Measurement – Clustering Approach

2018 ◽  
Vol 66 (2) ◽  
pp. 561-569 ◽  
Author(s):  
David Schüller ◽  
Jan Pekárek
Keyword(s):  
Linear Regression ◽  
Customer Satisfaction ◽  
Hierarchical Clustering ◽  
Theory And Practice ◽  
Coefficient Of Determination ◽  
Individual Factors ◽  
Marketing Theory ◽  
Linear Regression Models ◽  
Satisfaction Measurement ◽  
Customer Satisfaction Measurement

The paper deals with the issue of customer satisfaction measurement. The aim of this study is to determine the importance of the individual factors and their impact on total customer satisfaction for multiple segments by using linear regression and hierarchical clustering. This study is focused on the market of café establishment. We applied hierarchical clustering with Ward’s criterion to partition customers into segments and then we developed linear regression models for each segment. Linear models for partitioned data showed higher coefficient of determination than the model for the whole market. The results revealed that there are quite significant differences in rankings of customer satisfaction factors among the segments. This is caused by the different preferences of customers. The clustered data allows to achieve a higher homogeneity of data within the segment, which is crucial both for marketing theory and practice. The approach i.e. partitioning the market into smaller more specific segments could become perspective for marketing use in different economic sectors. This attitude can allow marketers to target better on customer segments according to the importance of individual factors.

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