Structural Parameter Identification in the Frequency Domain: The Use of Overdetermined Systems

1987 ◽  
Vol 109 (2) ◽  
pp. 120-123 ◽  
Author(s):  
S. G. Braun ◽  
Y. M. Ram
Keyword(s):  
Transfer Function ◽  
Parameter Identification ◽  
Frequency Domain ◽  
Rational Function ◽  
Least Square ◽  
Structural Parameter ◽  
Overdetermined Systems ◽  
The Matrix ◽  
Domain Transfer

This paper deals with the fitting of a rational function to an experimentally determined frequency domain transfer function. Examples show that the use of overdetermined fitted systems improve the identification in noisy situations. A method is presented, enabling the determination of the number of zero/poles of the system, and the relation to the rank of the matrix used in a least square identification method.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

Fourier Series-Based Neural Networks for Vehicle System Identification

1999 ◽  
Author(s):  
Imtiaz Haque ◽  
Juergen Schuller
Keyword(s):  
Neural Networks ◽  
Fourier Series ◽  
System Identification ◽  
Transfer Function ◽  
Parameter Identification ◽  
Frequency Domain ◽  
Vehicle System ◽  
Non Linear ◽  
Function Identification ◽  
Non Linear System

Abstract The use of neural networks in system identification is an emerging field. Neural networks have become popular in recent years as a means to identify linear and non-linear systems whose characteristics are unknown. The success of sigmoidal networks in parameter identification has been limited. However, harmonic activation-based neural networks, recent arrivals in the field of neural networks, have shown excellent promise in linear and non-linear system parameter identification. They have been shown to have excellent generalization capability, computational parallelism, absence of local minima, and good convergence properties. They can be used in the time and frequency domain. This paper presents the application of a special class of such networks, namely Fourier Series neural networks (FSNN) to vehicle system identification. In this paper, the applications of the FSNNs are limited to the frequency domain. Two examples are presented. The results of the identification are based on simulation data. The first example demonstrates the transfer function identification of a two-degree-of freedom lateral dynamics model of an automobile. The second example involves transfer function identification for a quarter car model. The network set-up for such identification is described. The results of the network identification are compared with theory. The results indicate excellent prediction properties of such networks.

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