Full-scale modal testing of a Hawk T1A aircraft for benchmarking vibration-based methods

Research developments for structural dynamics in the fields of design, system identification and structural health monitoring (SHM) have dramatically expanded the bounds of what can be learned from measured vibration data. However, significant challenges remain in the tasks of identification, prediction and evaluation of full-scale structures. A significant aid in the roadmap to the application of cutting-edge methods to the demands of in-service engineering structures, is the development of comprehensive benchmark datasets. With the aim of developing a useful and worthwhile benchmark dataset for structural dynamics, an extensive testing campaign is presented here. This recent campaign was performed on a decommissioned BAE system Hawk T1A aircraft at the Laboratory for Verification and Validation (LVV) in Sheffield. The aim of this paper is to present the dataset, providing details on the structure, experimental design, and data acquired. The collected data is made freely and openly available with the intention that it serve as a benchmark dataset for challenges in full-scale structural dynamics. Here, the details pertaining to two test phases (frequency and time domain) are presented. So as to ensure that the presented dataset is able to function as a benchmark, some baseline-level results are additionally presented for the tasks of identification and prediction, using standard approaches. It is envisaged that advanced methodologies will demonstrate superiority by favourable comparison with the results presented here. Finally, some dataset-specific challenges are described, with a view to form a hierarchy of tasks and frame discussion over their relative difficulty

On affine symbolic regression trees for the solution of functional problems

Symbolic regression has emerged from the more general method of Genetic Programming (GP) as a means of solving functional problems in physics and engineering, where a functional problem is interpreted here as a search problem in a function space. A good example of a functional problem in structural dynamics would be to find an exact solution of a nonlinear equation of motion. Symbolic regression is usually implemented in terms of a tree representation of the functions of interest; however, this is known to produce search spaces of high dimension and complexity. The aim of this chapter is to introduce a new representation—the affine symbolic regression tree. The search space size for the new representation is derived, and the results are compared to those for a standard regression tree. The results are illustrated by the search for an exact solution to several benchmark problems

On the dynamic properties of statistically-independent nonlinear normal modes

Much attention has been given to the study of nonlinear normal modes (NNMs), a nonlinear extension to the eminently useful framework for the analysis of linear dynamics provided by linear modal analysis (LMA). In the literature, several approaches have gained traction, with each able to preserve a subset of the useful properties of LMA. A recently-proposed framework (Worden and Green, 2017) casts nonlinear modal analysis as a problem in machine learning, viewing the NNM as directions in a latent modal coordinate space within which the modal dynamics are statistically uncorrelated. Thus far, the performance of this framework has been measured in a largely qualitative way. This paper presents, for the first time, an exploration into the underlying dynamics of the statistically-independent NNMs using techniques from nonlinear system identification (NLSI) and higher-order frequency-response functions (HFRFs). In this work, the statistically-uncorrelated NNMs are found for two simulated nonlinear cubic-stiffness systems using a recently-proposed neural-network based approach. NLSI models are fitted to both physical and modal displacements and the HFRFs of these models are compared to theoretical values. In particular, it is found for both systems that the modal decompositions here permit an independent single-input single-output (SISO) representation that can be projected back onto the original displacements with low error. It is also shown via the HFRFs that the underlying linear natural frequencies of the modal dynamics lie very close to the underlying linear natural frequencies of the nonlinear systems, indicating that a true nonlinear decomposition has been identified

On the vulnerability of data-driven structural health monitoring models to adversarial attack

Many approaches at the forefront of structural health monitoring rely on cutting-edge techniques from the field of machine learning. Recently, much interest has been directed towards the study of so-called adversarial examples; deliberate input perturbations that deceive machine learning models while remaining semantically identical. This article demonstrates that data-driven approaches to structural health monitoring are vulnerable to attacks of this kind. In the perfect information or ‘white-box’ scenario, a transformation is found that maps every example in the Los Alamos National Laboratory three-storey structure dataset to an adversarial example. Also presented is an adversarial threat model specific to structural health monitoring. The threat model is proposed with a view to motivate discussion into ways in which structural health monitoring approaches might be made more robust to the threat of adversarial attack

On the application of generative adversarial networks for nonlinear modal analysis

Linear modal analysis is a useful and effective tool for the design and analysis of structures. However, a comprehensive basis for nonlinear modal analysis remains to be developed. In the current work, a machine learning scheme is proposed with a view to performing nonlinear modal analysis. The scheme is focussed on defining a one-to-one mapping from a latent ‘modal’ space to the natural coordinate space, whilst also imposing orthogonality of the mode shapes. The mapping is achieved via the use of the recently-developed cycle-consistent generative adversarial network (cycle-GAN) and an assembly of neural networks targeted on maintaining the desired orthogonality. The method is tested on simulated data from structures with cubic nonlinearities and different numbers of degrees of freedom, and also on data from an experimental three-degree-of-freedom set-up with a column-bumper nonlinearity. The results reveal the method’s efficiency in separating the ‘modes’. The method also provides a nonlinear superposition function, which in most cases has very good accuracy