scholarly journals Entropy and multivariable interpolation

2006 ◽  
Vol 184 (868) ◽  
pp. 0-0 ◽  
Author(s):  
Gelu Popescu
Keyword(s):  
Multivariable Interpolation

Multivariable interpolation by weighted arithmetic means at arbitrary points

CALCOLO ◽  
1992 ◽  
Vol 29 (3-4) ◽  
pp. 301-311 ◽  
Author(s):  
G. Allasia ◽  
R. Besenghi ◽  
V. Demichelis
Keyword(s):  
Arithmetic Means ◽  
Weighted Arithmetic ◽  
Multivariable Interpolation

scholarly journals Use of Multiquadric Functions for Multivariable Representation of the Aerodynamic Coefficients of Airfoils

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Filipe Ribeiro ◽  
Pedro Albuquerque ◽  
Pedro Gamboa ◽  
Kouamana Bousson
Keyword(s):  
Radial Basis Functions ◽  
Piecewise Linear ◽  
Research Work ◽  
Computational Cost ◽  
Basis Functions ◽  
Aerodynamic Coefficients ◽  
Independent Variables ◽  
Advantages And Disadvantages ◽  
Radial Basis ◽  
Multivariable Interpolation

Given an array (or matrix) of values for a function of one or more variables, it is often desired to find a value between two given points. Multivariable interpolation and approximation by radial basis functions are important subjects in approximation theory that have many applications in Science and Engineering fields. During the last decades, radial basis functions (RBFs) have found increasingly widespread use for functional approximation of scattered data. This research work aims at benchmarking two different approaches: an approximation by radial basis functions and a piecewise linear multivariable interpolation in terms of their effectiveness and efficiency in order to conclude about the advantages and disadvantages of each approach in approximating the aerodynamic coefficients of airfoils. The main focus of this article is to study the main factors that affect the accuracy of the multiquadric functions, including the location and quantity of centers and the choice of the form factor. It also benchmarks them against piecewise linear multivariable interpolation regarding their precision throughout the selected domain and the computational cost required to accomplish a given amount of solutions associated with the aerodynamic coefficients of lift, drag and pitching moment. The approximation functions are applied to two different multidimensional cases: two independent variables, where the aerodynamic coefficients depend on the Reynolds number (Re) and the angle-of-attack (α), and four independent variables, where the aerodynamic coefficients depend on Re, α, flap chord ratio (cflap), and flap deflection (δflap).

scholarly journals Visual Biofeedback Tool for Quantitative Pressure Monitoring in Lower-Limb Prosthetic Sockets

2021 ◽  
Author(s):  
Shruti Turner ◽  
Shivali Jain ◽  
Akhil Patel ◽  
Matthew O Hopkins ◽  
Alison H McGregor
Keyword(s):  
Interpolation Method ◽  
Pressure Sensors ◽  
Pressure Data ◽  
Prosthetic Socket ◽  
Visual Biofeedback ◽  
Desktop Application ◽  
Test Pressure ◽  
Data Points ◽  
Multivariable Interpolation ◽  
Data Updating

Obtaining a good socket fit is an iterative process dependent on the skill and experience of the prosthetist creating it, and requiring individualisation based on the size and shape. There is no standard measurement system used to aid prosthetic socket creation, despite the severe impacts on physical health and quality of life if one is ill-fitting. Pressure sensors embedded in a prosthetic socket were used to collect data at the socket-residuum interface. To choose an interpolation method, a 2D grid was used, with previously collected walking test pressure data, to simplify the sensor array with a border for extrapolation. Four multivariable interpolation methods were evaluated to create a colour map of the pressure data. Radial Basis Function interpolation was chosen as it produced a clear image with a graduated interpolation between data points and was used to create a colour map across the surface of a 3D prosthetic socket model. For the model to be accessible to clinical audiences, a desktop application was created using PyQt to view the model. The created application allowed for connection to the sensors via Bluetooth, with the pressure data updating the colour map on the 3D model in real-time. The created application shows the potential for a clinical product, however further development informed by feedback from rehabilitation clinicians and prosthesis users is required

scholarly journals A Visual Feedback Tool for Quantitative Pressure Monitoring in Lower-Limb Prosthetic Sockets

Prosthesis ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 394-405
Author(s):  
Shruti Turner ◽  
Shivali Jain ◽  
Akhil Patel ◽  
Matthew O. Hopkins ◽  
Alison H. McGregor
Keyword(s):  
Interpolation Method ◽  
Pressure Sensors ◽  
Pressure Data ◽  
Prosthetic Socket ◽  
Desktop Application ◽  
Test Pressure ◽  
Data Points ◽  
Multivariable Interpolation ◽  
Data Updating

Obtaining a good socket fit is an iterative process dependent on the skill and experience of the prosthetist creating it and requires individualisation based on the size and shape. There is no standard measurement system used to aid prosthetic socket creation despite the severe impacts on physical health and quality of life if one is ill fitting. Pressure sensors embedded in a prosthetic socket were used to collect data at the socket–residuum interface. To choose an interpolation method, the sensor array was simplified to a 2D grid with a border for extrapolation and tested using previously collected walking test pressure data. Four multivariable interpolation methods were evaluated to create a colour map of the pressure data. Radial basis function interpolation was chosen, as it produced a clear image with a graduated interpolation between data points, and was used to create a colour map across the surface of a 3D prosthetic socket model. For the model to be accessible to clinical audiences, a desktop application was created using PyQt to view the model. The application allowed for connection to the sensors via Bluetooth, with the pressure data updating on the 3D model in real time. Clinician feedback on the application showed the potential for a clinical product; however, further development informed by feedback from rehabilitation clinicians and prosthesis users is required.

Sign in / Sign up

Export Citation Format

Share Document