Parametric and nonparametric identification of nonlinearity in structural dynamics

The work described in this thesis is concerned with procedures for the identification of nonlinearity in structural dynamics. It begins with a diagnostic method which uses the Hubert transform for detecting nonlinearity and describes the neccessary conditions for obtaining a valid Hubert transform. The transform is shown to be incapable of producing a model with predictive power. A method based on the identification of nonlinear restoring forces is adopted for extracting a nonlinear model. The method is critically examined; various caveats, modifications and improvements are obtained. The method is demonstrated on time data obtained from computer simulations. It is shown that a parameter estimation approach to restoring force identification based on direct least—squares estimation theory is a fast and accurate procedure. In addition, this approach allows one to obtain the equations of motion for a multi—degree—of—freedom system even if the system is only excited at one point. The data processing methods for the restoring force identification including integration and differentiation of sampled time data are developed and discussed in some detail. A comparitive study is made of several of the most well—known least—squares estimation procedures and the direct least —squares approach is applied to data from several experiments where it is shown to correctly identify nonlinearity in both single— and multi—degree--of—freedom systems. Finally, using both simulated and experimental data, it is shown that the recursive least—squares algorithm modified by the inclusion of a data forgetting factor can be used to identify time—dependent structural parameters.Science and Engineering Research Counci

On topological data analysis for structural dynamics: an introduction to persistent homology

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be introduced. The main tool within topological data analysis (TDA) is persistent homology. Persistent homology is a method of quantifying the shape of data over a range of length scales. The required background and a method of computing persistent homology is briefly discussed in this work. Ideas from topological data analysis are then used for nonlinear dynamics to analyse some common attractors, by calculating their embedding dimension, and then to assess their general topologies. A method will also be proposed, that uses topological data analysis to determine the optimal delay for a time-delay embedding. TDA will also be applied to a Z24 Bridge case study in structural health monitoring, where it will be used to scrutinise different data partitions, classified by the conditions at which the data were collected. A metric, from topological data analysis, is used to compare data between the partitions. The results presented demonstrate that the presence of damage alters the manifold shape more significantly than the effects present from temperature

uncertainty bounds on higher order frfs from gaussian process narx models

One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. In recent papers, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression and derived the corresponding expressions for Higher-order Frequency Response Functions (HFRFs). This paper extends the theory for the GP-NARX framework by providing a means of converting the GP prediction bounds in the time domain into bounds on the HFRFs. The approach is demonstrated on the Duffing oscillator

Experimental studies on impact damage location in composite aerospace structures using genetic algorithms and neural networks

Impact damage detection in composite structures has gained a considerable interest in many engineering areas. The capability to detect damage at the early stages reduces any risk of catastrophic failure. This paper compares two advanced signal processing methods for impact location in composite aircraft structures. The first method is based on a modified triangulation procedure and Genetic Algorithms whereas the second technique applies Artificial Neural Networks. A series of impacts is performed experimentally on a composite aircraft wing�box structure instrumented with low-profile, bonded piezoceramic sensors. The strain data are used for learning in the Neural Network approach. The triangulation procedure utilises the same data to establish impact velocities for various angles of strain wave propagation. The study demonstrates that both approaches are capable of good impact location estimates in this complex structure

Towards risk-informed PBSHM: Populations as hierarchical systems

The prospect of informed and optimal decision-making regarding the operation and maintenance (O&M) of structures provides impetus to the development of structural health monitoring (SHM) systems. A probabilistic risk-based framework for decision-making has already been proposed. However, in order to learn the statistical models necessary for decision-making, measured data from the structure of interest are required. Unfortunately, these data are seldom available across the range of environmental and operational conditions necessary to ensure good generalisation of the model. Recently, technologies have been developed that overcome this challenge, by extending SHM to populations of structures, such that valuable knowledge may be transferred between instances of structures that are sufficiently similar. This new approach is termed population-based structural heath monitoring (PBSHM). The current paper presents a formal representation of populations of structures, such that risk-based decision processes may be specified within them. The population-based representation is an extension to the hierarchical representation of a structure used within the probabilistic risk-based decision framework to define fault trees. The result is a series, consisting of systems of systems ranging from the individual component level up to an inventory of heterogeneous populations. The current paper considers an inventory of wind farms as a motivating example and highlights the inferences and decisions that can be made within the hierarchical representation.Comment: Submitted to IMAC-XLI conference (2023), Austin, Texas, US

Simulation of ultrasonic lamb wave generation, propagation and detection for an air coupled robotic scanner

A computer simulator, to facilitate the design and assessment of a reconfigurable, air-coupled ultrasonic scanner is described and evaluated. The specific scanning system comprises a team of remote sensing agents, in the form of miniature robotic platforms that can reposition non-contact Lamb wave transducers over a plate type of structure, for the purpose of non-destructive evaluation (NDE). The overall objective is to implement reconfigurable array scanning, where transmission and reception are facilitated by different sensing agents which can be organised in a variety of pulse-echo and pitch-catch configurations, with guided waves used to generate data in the form of 2-D and 3-D images. The ability to reconfigure the scanner adaptively requires an understanding of the ultrasonic wave generation, its propagation and interaction with potential defects and boundaries. Transducer behaviour has been simulated using a linear systems approximation, with wave propagation in the structure modelled using the local interaction simulation approach (LISA). Integration of the linear systems and LISA approaches are validated for use in Lamb wave scanning by comparison with both analytic techniques and more computationally intensive commercial finite element/difference codes. Starting with fundamental dispersion data, the paper goes on to describe the simulation of wave propagation and the subsequent interaction with artificial defects and plate boundaries, before presenting a theoretical image obtained from a team of sensing agents based on the current generation of sensors and instrumentation

Sensor Validation for On-line Vibration Monitoring

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or maintenance activities. The problem of sensor validation is therefore a critical part or structural identification. The objective of the present study is to present a procedure based on principal component analysis, which is able to perform detection, isolation and reconstruction of a faulty sensor. Its e ciency is assessed using an experimental application