scholarly journals Radial Basis Functions Intended to Determine the Upper Bound of Absolute Dynamic Error at the Output of Voltage-Mode Accelerometers

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4154 ◽  
Author(s):  
Krzysztof Tomczyk ◽  
Marcin Piekarczyk ◽  
Grzegorz Sokal
Keyword(s):  
Mathematical Model ◽  
Radial Basis Functions ◽  
Upper Bound ◽  
Dynamic Error ◽  
Basis Functions ◽  
Voltage Mode ◽  
Radial Basis ◽  
Operational Frequency ◽  
Mc Method

In this paper, we propose using the radial basis functions (RBF) to determine the upper bound of absolute dynamic error (UAE) at the output of a voltage-mode accelerometer. Such functions can be obtained as a result of approximating the error values determined for the assumed-in-advance parameter variability associated with the mathematical model of an accelerometer. This approximation was carried out using the radial basis function neural network (RBF-NN) procedure for a given number of the radial neurons. The Monte Carlo (MC) method was also applied to determine the related error when considering the uncertainties associated with the parameters of an accelerometer mathematical model. The upper bound of absolute dynamic error can be a quality ratio for comparing the errors produced by different types of voltage-mode accelerometers that have the same operational frequency bandwidth. Determination of the RBFs was performed by applying the Python-related scientific packages, while the calculations related both to the UAE and the MC method were carried out using the MathCad program. Application of the RBFs represent a new approach for determining the UAE. These functions allow for the easy and quick determination of the value of such errors.

Determination of multiple direction of arrival in antennas arrays with radial basis functions

2006 ◽  
Vol 70 (1-3) ◽  
pp. 55-61 ◽  
Author(s):  
Osmar de Araújo Dourado Júnior ◽  
Adrião Duarte Dória Neto ◽  
Wilson da Mata
Keyword(s):  
Radial Basis Functions ◽  
Direction Of Arrival ◽  
Basis Functions ◽  
Radial Basis

AUTOMATIC DETERMINATION OF RADIAL BASIS FUNCTIONS: AN IMMUNITY-BASED APPROACH

2001 ◽  
Vol 11 (06) ◽  
pp. 523-535 ◽  
Author(s):  
LEANDRO NUNES DE CASTRO ◽  
FERNANDO J. VON ZUBEN
Keyword(s):  
Radial Basis Functions ◽  
Rbf Neural Network ◽  
Basis Functions ◽  
Classification Problems ◽  
Selection Procedures ◽  
Rbf Network ◽  
Radial Basis ◽  
Optimal Set ◽  
Unsupervised Cluster Analysis

The appropriate operation of a radial basis function (RBF) neural network depends mainly upon an adequate choice of the parameters of its basis functions. The simplest approach to train an RBF network is to assume fixed radial basis functions defining the activation of the hidden units. Once the RBF parameters are fixed, the optimal set of output weights can be determined straightforwardly by using a linear least squares algorithm, which generally means reduction in the learning time as compared to the determination of all RBF network parameters using supervised learning. The main drawback of this strategy is the requirement of an efficient algorithm to determine the number, position, and dispersion of the RBFs. The approach proposed here is inspired by models derived from the vertebrate immune system, that will be shown to perform unsupervised cluster analysis. The algorithm is introduced and its performance is compared to that of the random, k-means center selection procedures and other results from the literature. By automatically defining the number of RBF centers, their positions and dispersions, the proposed method leads to parsimonious solutions. Simulation results are reported concerning regression and classification problems.

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