Constructing an overall dynamical model for a system with changing design parameter properties

This study considers the identification problem for a class of non-linear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient Common Model Structure Selection (CMSS) algorithm, called the Extended Forward Orthogonal Regression (EFOR) algorithm, is proposed to select such a common model structure. Two examples are presented to illustrate the application and the effectiveness of the new identification approach

Truncation of Nonlinear System Expansions in the Frequency Domain

The truncation of Volterra series expansions is studied using the output frequency characteristics of nonlinear systems to develop a new algorithm for determining the terms to include in a Volterra series expansion. The results show the influence of both the generalised frequency response functions and properties of the input spectra on the significance of individual terms in the series. The effectiveness of the proposed method is demonstrated using simulation studies including the analysis of a single degree mechanical oscillator. Because nonlinear system analysis using Volterra series theory must always be based on a truncated Volterra series description, the present study provides an effective strategy for determining which terms to include in the analysis of practical nonlinear systems based on the Volterra series models

Evaluation of Output Frequency Responses of Nonlinear Systems Under Multiple Inputs

In this paper, a new method for evaluating output frequency responses of nonlinear systems under multiple inputs is developed based on two theoretical results concerning the output frequency responses of nonlinear systems to multiple inputs and the determination of output frequencies of nonlinear systems subject to multiple input excitations. This method circumvents difficulties associated with the existing "frequency mix vector" based approaches and can be applied to evaluate nonlinear output frequency responses to multiple inputs so as to investigate nonlinear behaviours of practical systems including electronic circuits at the system simulation and design stages

Modeling and frequency domain analysis of nonlinear compliant joints for a passive dynamic swimmer

In this paper we present the study of the mathematical model of a real life joint used in an underwater robotic fish. Fluid-structure interaction is utterly simplified and the motion of the joint is approximated by D\"uffing's equation. We compare the quality of analytical harmonic solutions previously reported, with the input-output relation obtained via truncated Volterra series expansion. Comparisons show a trade-off between accuracy and flexibility of the methods. The methods are discussed in detail in order to facilitate reproduction of our results. The approach presented herein can be used to verify results in nonlinear resonance applications and in the design of bio-inspired compliant robots that exploit passive properties of their dynamics. We focus on the potential use of this type of joint for energy extraction from environmental sources, in this case a K\'arm\'an vortex street shed by an obstacle in a flow. Open challenges and questions are mentioned throughout the document.Comment: 12 p, 5 fig, work in progress, collaborative wor

Vibration Control of Systems in Presence of Hard Nonlinearities

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An Investigation into the Characteristics of Nonlinear Frequency Response Functions, Part 2; New Analysis Methods Based on Symbolic Expansions and Graphical Techniques

In Part 1 of this paper the concepts of input and output frequency subdomains were introduced to give insight into the relation between one dimensional and multi-dimensional frequency spaces. The visualisation of both magnitude and phase responses of third order generalised frequency response functions was also presented. In this, the secind part, symbolic expansion techniques are introduced and together with the results achieved in Part 1, yield new methods for analysing the properties of generalised frequency response functions. Case studies are included to illustrate the application of the new methods

An Investigation into the Characteristics of Nonlinear Frequency Response Functions, Part 1: Understanding the Higher Dimensional Frequency Spaces

The characteristics of generalised frequency response functions (GFRF's) of nonlinear systems in higher dimensional space are investigated using a combination of graphical and symbolic decomposition techniques. It is shown how a systematic analysis can be achieved for a wide class of nonlinear systems in the frequency domain using the proposed methods. The paper is divided into two parts. In Part 1, the concepts of input and output frequency subdomains are introduced to give insight into the relationship between one dimensional and multi-dimensional frequency spaces. The visualisation of both magnitude and phase-responses of third order generalised frequency response functions is presented for the first time. In Part 2 symbolic expansion techniques are introduced and new methods are developed to analyse the properties of generalised frequency response functions of nonlinear systems described by the NARMAX class of models. Case studies are included in Part 2 to illustrate the application of new methods

Output frequency response function-based analysis for nonlinear Volterra systems

Analysis of nonlinear systems has been studied extensively. Based on some recently developed results, a new systematic approach to the analysis of nonlinear Volterra systems in the frequency domain is proposed in this paper, which provides a novel insight into the frequency domain analysis and design of nonlinear systems subject to a general input instead of only specific harmonic inputs using input-output experimental data. A general procedure to conduct an output frequency response function (OFRF) based analysis is given, and some fundamental results and techniques are established for this purpose. A case study for the analysis of a circuit system is provided to illustrate this new frequency domain method

System identification-based frequency domain feature extraction for defect detection and characterization

Feature extraction is the key step for defect detection in Non-Destructive Evaluation (NDE) techniques. Conventionally, feature extraction is performed using only the response or output signals from a monitoring device. In the approach proposed in this paper, the NDE device together with the material or structure under investigation are viewed as a dynamic system and the system identification techniques are used to build a parametric dynamic model for the system using the measured system input and output data. The features for defect detection and characterization are then selected and extracted from the frequency response function (FRF) derived from the identified dynamic model of the system. The new approach is validated by experimental studies with two different types of NDE techniques and the results demonstrate the advantage and potential of using control engineering-based approach for feature extraction and quantitative NDE. The proposed approach offers a general framework for selection and extraction of the dynamic property-related features of structures for defect detection and characterization, and provides a useful alternative to the existing methods with a potential of improving NDE performance