R. J. Barthorpe

Identification of Hysteretic Systems Using NARX Models, Part I: Evolutionary Identification

Although there has been considerable work on the identification of hysteretic systems over the years, there has been comparatively little using discrete NARX or NARMAX models. One of the reasons for this may be that many of the common continuous-time models for hysteresis, like the Bouc-Wen model are nonlinear in the parameters and incorporate unmeasured states, and this makes a direct analytical discretisation somewhat opaque. Because NARX models are universal in the sense that they can model any input–output process, they can be applied directly without consideration of the hysteretic nature; however, if the polynomial form of NARX were to be used for a Bouc-Wen system, the result would be input-dependent because of the non-polynomial (indeed discontinuous) nature of the original model. The objective of the current paper is to investigate the use of NARX models for Bouc-Wen systems and to consider the use of non-polynomial basis functions as a potential means of alleviating any input-dependence. As the title suggests, the parameter estimation scheme adopted will be an evolutionary one based on Self-Adaptive Differential Evolution (SADE). The paper will present results for simulated data.

Novelty detection applied to vibration data from a CX-100 wind turbine blade under fatigue loading

The remarkable evolution of new generation wind turbines has led to a dramatic increase of wind turbine blade size. In turn, a reliable structural health monitoring (SHM) system will be a key factor for the successful implementation of such systems. Detection of damage at an early stage is a crucial issue as blade failure would be a catastrophic result for the entire wind turbine. In this study the SHM analysis will be based on experimental measurements of Frequency Response Functions (FRFs) extracted by using an input/output acquisition technique under a fatigue loading of a 9m CX-100 blade at the National Renewable Energy Laboratory (NREL) and National Wind Technology Center (NWTC) performed in the Los Alamos National Laboratory. The blade was harmonically excited at its first natural frequency using a Universal Resonant Excitation (UREX) system. For analysis, the Auto-Associative Neural Network (AANN) is a non-parametric method where a set of damage sensitive features gathered from the measured structure are used to train a network that acts as a novelty detector. This traditionally has a highly complex bottleneck structure with five layers in the AANN. In the current paper, a new attempt is also exploited based on an AANN with one hidden layer in order to reduce the theoretical and computational difficulties. Damage detection of composite bodies of blades is a grand challenge due to varying aerodynamic and gravitational loads and environmental conditions. A study of the noise tolerant capability of the AANN which is associated to its generalisation capacity is addressed. It will be shown that vibration response data combined with AANNs is a robust and powerful tool, offering novelty detection even when operational and environmental variations are present. The AANN is a method which has not yet been widely used in the structural health monitoring of composite blades.

Advanced Feature Selection for Simplified Pattern Recognition within the Damage Identification Framework

The paper is concerned with adopting a data-driven approach to damage detection and location on an aerospace structure without recourse to an artificial neural network. Five advanced features are selected, each detecting the removal of only one of five inspection panels on the structure. The features give perfect classification for damage location for single-site damage and 98.1% correct classification for multi-site damage scenarios, using a statistically calculated threshold. However, if the threshold values for two of the five features are altered slightly, 100% correct classification would be possible for single- and multi-site damage.

Nonlinear Modal Interaction Analysis for a Three Degree-of-Freedom System with Cubic Nonlinearities

The majority of work in the literature on modal interaction is based on two degree-of-freedom nonlinear systems with cubic nonlinearities. In this paper we consider a three degree-of-freedom system with nonlinear springs containing cubic nonlinear terms. First the undamped, unforced case is considered. Specifically the modal interaction case that occurs when all the underlying linear modal frequencies are close is considered (i.e. \(\omega _{n1}:\omega _{n2}:\omega _{n3} \simeq 1: 1: 1\)). In the case considered, due to the symmetry of the system, the first mode is linear and not coupled with the other two modes. The analysis is carried out by using a normal form transformation to obtain the nonlinear backbone curves of the undamped, unforced response. In addition, the frequency response function (FRF) of the corresponding lightly damped and harmonically forced system obtained from the continuation software AUTO-07p is compared with the backbone curves to show its validity for predicting the nonlinear resonant frequency and amplitude. A comparison of the results gives an insight into how modal interactions in the forced-damped response can be predicted using just the backbone curves, and how this might be applied to predict resonant responses of multi-modal nonlinear systems more generally.

Bayesian System Identification of Dynamical Systems Using Reversible Jump Markov Chain Monte Carlo

The purpose of this contribution is to illustrate the potential of Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods for nonlinear system identification. Markov Chain Monte Carlo (MCMC) sampling methods have come to be viewed as a standard tool for tackling the issue of parameter estimation using Bayesian inference. A limitation of standard MCMC approaches is that they are not suited to tackling the issue of model selection. RJMCMC offers a powerful extension to standard MCMC approaches in that it allows parameter estimation and model selection to be addressed simultaneously. This is made possible by the fact that the RJMCMC algorithm is able to “jump” between parameter spaces of varying dimension. In this paper the background theory to the RJMCMC algorithm is introduced. Comparison is made to a standard MCMC approach.

Machine Learning Applications for a Wind Turbine Blade under Continuous Fatigue Loading

Structural health monitoring (SHM) systems will be one of the leading factors in the successful establishment of wind turbines in the energy arena. Detection of damage at an early stage is a vital issue as blade failure would be a catastrophic result for the entire wind turbine. In this study the SHM analysis will be based on experimental measurements of vibration analysis, extracted of a 9m CX-100 blade under fatigue loading. For analysis, machine learning techniques utilised for failure detection of wind turbine blades will be applied, like non-linear Neural Networks, including Auto-Associative Neural Network (AANN) and Radial Basis Function (RBF) networks models.

Classification of multi-site damage using support vector machines

Pattern recognition is now well-known to be a powerful approach to addressing the higher levels of damage identification e.g. location and severity assessment of damage. However, a major problem in implementation for real structures is the need for training data associated with all possible damage states. Even if appropriate data were available for individual damage states, the combinatorial explosion in states which occurs when multiple simultaneous damages are present would usually prohibit a pattern recognition approach. One approach to the solution of this problem is to construct classifiers on the basis of single damage data which will generalise to multiple damage states; the current paper is a very preliminary step in this direction. In the first part, a comprehensive multiple damage feature database is established as the result of an experimental campaign on a full-sized aircraft wing structure; in the second part, a classifier based on the support vector machine paradigm is investigated. The paper also considers how data visualisation can shed light on which features are likely to generalise best from the single damage problem to the multiple damage case.

An Experimental Investigation of Feature Availability in Nominally Identical Structures for Population-Based SHM

It is perhaps well known that the uncertainty in realistic structures may complicate most efforts for modelling and damage identification. In a population of structures which are considered identical, as in a wind farm for example, it is very often that the accurate modelling of one structure will be inadequate for the robust monitoring of the rest in an SHM approach. This paper presents an exploration of the common features which can be found in nominally identical structures and which can be used for damage identification with the ultimate purpose of population-based SHM. The concept of a population-based approach means that any additional new structures to the population will not need to be fully modelled in order to be monitored. Two different variants of the tail wing of a Piper PA-28 aircraft are used to create two pairs of nominally identical structures by separating the tail wings in half. The new population of four structures thus contains two pairs of them which are similar, but they have different length and different weight. A full modal test is performed in all of the structures and an exploration of possible common features is also done. The results show that common damage-sensitive features exist across the structures, a key requirement if population-based SHM is to be successfull.

An SHM View of a CFD Model of Lillgrund Wind Farm

Reliability of offshore wind farms is one of the key areas for the successful implementation of these renewable power plants in the energy arena. Failure of the wind turbine (WT) in general could cause massive financial losses but especially for structures that are operating in offshore sites. Structural Health Monitoring (SHM) of WTs is essential in order to ensure not only structural safety but also avoidance of overdesign of components that could lead to economic and structural inefficiency. A preliminary analysis of a machine learning approach in the context of WT SHM is presented here; it is based on results from a Computational Fluid Dynamics (CFD) model of Lillgrund Wind farm. The analysis is based on neural network regression and is used to predict the measurement of each WT from the measurements of other WTs in the farm. Regression model error is used as an index of abnormal response.

Comparative Study of Robust Novelty Detection Techniques

The central target of this work is to provide an alternative to machine learning approaches to structural health monitoring with one of robust multivariate statistic novelty detection. Damage detection and identification is a procedure that is hierarchical in nature. At its most sophisticated, diagnosis of the damage could include localisation, classification and severity assessment and even go so far as to estimate the time-to-failure of the structure. In this paper, robust multivariate statistics were investigated focused mainly on a high level estimation of the outliers which determines only the presence or absence of novelty - something that is of fundamental interest. These methods allow a diagnosis of deviation from normality and the option of identifying the presence of masking effects caused by multiple outliers. This paper is trying to introduce a new scheme for damage detection by adopting simple measurements and exploiting robust multivariate statistics.