Consolidating guided wave simulations and experimental data: a dictionary learning approach

A semi-analytical wavelet finite element method for wave propagation in rectangular rods

Ultrasonic guided-wave (UGW) NDT technology is an efficient means for damage identification and has been applied widely in the field of detection for pipelines, railway tracks, ships and aircrafts. Besides, the dispersion curves of the guided waves in a square steel pipe are indispensable references for the integrity test of continuous structural components, which represent the frequency dependence of guided wave velocities. Unfortunately, the complete dispersion curve of ultrasonic waves in square steel pipes cannot be solved by the traditional finite element modal analysis method. To address the problem, the semi-analytical finite element (SAFE) method was used to obtain the ultrasonic guided wave dispersion curves in a square steel pipe, on this basis, a UGW-based NDT strategy is proposed. Firstly, triangular elements are adopted to perform the finite element discretization on the cross-section of the square steel pipe, and the guided wave is assumed to be in a harmonic motion along the wave propagation direction. Then, the wave equation of the ultrasonic guided waves propagating in the square steel pipe is deduced theoretically, through solving the characteristic equation, the wave number and frequency can be obtained, and the relation between the frequency and phase velocity & group velocity is obtained; thus, the dispersion curves can be plotted, which can be used to analyze the vibration characteristics of the guided wave modes. Afterwards, the optimal excitation frequency, excitation direction and excitation location are selected based on dispersion property for the different damage modes of the square steel pipe. Lastly, the proposed damage identification method is validated through numerical simulation. The results show that the dispersion curves of square steel pipe solved with the semi-analytical finite element method are in good agreement with the simulated result, besides, for the damage on the square steel pipe surface, the reflected guided wave package can identify the damage location effectively under the selected excitation.

Guided wave propagation in composite pipe has multi-modal and dispersive characteristics. In this paper, guided wave propagation in composite pipe is solved by a semi-analytical finite element (SAFE) method. The theoretical framework is formulated using finite element method (FEM) to describe the displacement fields in the waveguide cross-section, while displacement fields in the wave propagation direction are assumed analytical solutions. The dispersive solutions are obtained in terms of phase velocity and group velocity. Knowledge of guided wave propagation properties in composite pipe is beneficial for practical nondestructive testing and structural health monitoring. The SAFE method is validated by comparison with numerical results by ABAQUS. Also, experimental results from group velocity measurement on a composite pipe are presented, showing the feasibility of this SAFE method.

Efficient wind energy harvesting becomes more and more important as a consequence of the increasing interest in renewable energy in the European Union [1]. This leads to growing sizes of wind turbines (WTs), and with it, larger WT blades (WTBs). The structural designs of these WTBs are created to optimize the potential energy output, where low mass is a key requirement. However, high flexibilities and lower buckling capacities are further results of these developments [2], thus certain damage scenarios become significant. Intelligently designed structural health monitoring (SHM) systems can help to reduce the associated operations and maintenance costs. Even though, several techniques are already developed for structural damage detection (SDD) in WTBs, the majority of these methods is not suitable for inservice measurements. This paper presents a SDD and structural damage localization (SDL) method based on the partial autocorrelation function (PACF) of vibration responses. The approach is applied to a numerical model of a large WTB, where the acceleration responses are obtained from transient dynamic simulations with a simplified aerodynamic loading approach. The novel damage sensitive feature (DSF) is developed as the Mahalanobis distance between a baseline and current vector of PACF coefficients. First, numerical modal analysis of the finite element (FE) WTB model is performed in order to estimate the effect of a disbonding damage scenario on the vibration characteristics. Second, the behaviour of the PACF for time series of the healthy system is discussed. Third, the SDD results on the basis of statistical hypothesis testing are assessed for two selected sensor locations and increasing damage extents. Finally, the performance of the proposed DSF with respect to SDL is illustrated for multiple locations on the WTB’s surface. This study demonstrated the efficiency of a DSF based on the PACF for SDD and SDL, which is promising for future developments of vibration-based SHM techniques in WTBs.

Piezoelectric Wafer Active Sensors (PWAS) are convenient enablers for generating and receiving ultrasonic guided waves. The wide application of composite structures has put new challenges for the Structural Health Monitoring (SHM) and Nondestructive Evaluation (NDE) community due to the general anisotropic behaviors and complicated guided wave features in composites. The excitability of guided waves in composite structures directly influences the implementation of active sensing systems to achieve the best interrogation of certain sensing directions. This paper presents a hybrid modeling technique for studying the excitably of guided waves in composite structures with PWAS transducers. This hybrid technique comprehensively covers local finite element model (FEM), semi-analytical finite element (SAFE) method, and analytical guided wave solutions. Harmonic analysis of a small-size local FEM with non-reflective boundaries (NRB) was carried out for obtaining guided wave generation features in plate structures. The PWAS transducers were modeled with coupled filed elements. Thus, the FEM can fully capture the geometry and material property effects of PWAS transducers and their influence on the guided wave excitation. SAFE method was used to obtain the complicated guided wave features in composites such as dispersion curves and modeshapes. The SAFE procedure was coded into MATLAB Graphical User Interface (GUI), and the software SAFE-DISPERSION was developed. To study the excitability of each wave mode, we considered all the possible wave modes being generated simultaneously and propagating independently. The analytical wave expressions based on the exact guided wave solution with Hankel functions were used to join the SAFE method and the local FEM. Formulated in frequency domain, the hybrid model is highly efficient, providing an over determined equation system for the calculation of mode participation factors. Case studies were carried out: (1) the Lamb wave excitability in an aluminum plate was investigated and compared with classical pin force models to show the feasibility of the hybrid technique; (2) the guided wave excitability in a woven glass fiber composite (GFRP) plate was studied with circular and square PWAS transducers. The paper finishes with summary, conclusions, and suggestions for future work.

The present thesis focuses on elastic waves behaviour in ordinary structures as well as in acousto-elastic metamaterials via numerical and experimental applications. After a brief introduction on the behaviour of elastic guided waves in the framework of non-destructive evaluation (NDE) and structural health monitoring (SHM) and on the study of elastic waves propagation in acousto-elastic metamaterials, dispersion curves for thin-walled beams and arbitrary cross-section waveguides are extracted via Semi-Analytical Finite Element (SAFE) methods. Thus, a novel strategy tackling signal dispersion to locate defects in irregular waveguides is proposed and numerically validated. Finally, a time-reversal and laser-vibrometry based procedure for impact location is numerically and experimentally tested. In the second part, an introduction and a brief review of the basic definitions necessary to describe acousto-elastic metamaterials is provided. A numerical approach to extract dispersion properties in such structures is highlighted. Afterwards, solid-solid and solid-fluid phononic systems are discussed via numerical applications. In particular, band structures and transmission power spectra are predicted for 1P-2D, 2P-2D and 2P-3D phononic systems. In addition, attenuation bands in the ultrasonic as well as in the sonic frequency regimes are experimentally investigated. In the experimental validation, PZTs in a pitch-catch configuration and laser vibrometric measurements are performed on a PVC phononic plate in the ultrasonic frequency range and sound insulation index is computed for a 2P-3D phononic barrier in the sonic frequency range. In both cases the numerical-experimental results comparison confirms the existence of the numerical predicted band-gaps. Finally, the feasibility of an innovative passive isolation strategy based on giant elastic metamaterials is numerically proved to be practical for civil structures. In particular, attenuation of seismic waves is demonstrated via finite elements analyses. Further, a parametric study shows that depending on the soil properties, such an earthquake-proof barrier could lead to significant reduction of the superstructure displacement.

Action recognition is still a challenging problem. In order to catch effective compact representation of the action sequences, the discriminative dictionaries could be learned by sparse coding. But sparse coding is needed in both the training and testing phases of the classifier framework. And it is also time consuming for the adoption of 1-norm sparsity constraint on the representation coefficients in most dictionary learning (DL) methods. Dictionary pair learning (DPL) learns a synthesis dictionary and an analysis dictionary jointly. Compared with those DL approaches, the using of DPL method may not only effectively reduce the time consuming during the phases of training and testing, but also result in very competitive recognition ratio. On the other hand, the way of compressed learning can lead to learning with randomly projected data instead of original data. Thus compressed learning could greatly cut down on both the requirement of memory storage and running time due to the effective reduction of data dimensions through random projection. In this paper, Combined with compressed learning, DPL in compressed space are explored for the action recognition. By the experiments on various public action datasets, it has been shown that DPL in compressed space can achieves very competitive accuracy, while it is significantly faster in phases of both training and testing, which indicate the efficiency of the proposed algorithm for action recognition.

Dictionary learning has played an important role in the success of sparse representation. Although several dictionary learning approaches have been developed for image classification, the dictionary pair learning, i.e., jointly learning a synthesis dictionary and an analysis dictionary, is still in its infant stage. In this paper, we proposed a novel model of dictionary pair learning with block-diagonal structure (DPL-BDS), in which a block-diagonal structure of coding coefficient matrix and a block-diagonal structure of analysis dictionary are enforced. With the block-diagonal structures, discrimination of synthesis dictionary representation, coding coefficients and analysis dictionary are introduced into the dictionary pair learning model. An iterative algorithm to efficiently solve the proposed DPL-BDS was presented in this paper. The experiments on face recognition, scene categorization, and action recognition clearly show the advantage of the proposed DPL-BDS.

The enormous potential of Guided waves have a significant use for non-destructive evaluation(NDE) and structural health monitoring(SHM). It is common to use different solution approaches to predict dispersion curves depending on the material type, isotropic, transversely isotropic, or orthotropic, of the medium in which the wave propagates, shape of the waveguide, etc. Inability to model waveguides of arbitrary cross-section by existing matrix methods has led to development of Semi-Analytical Finite Element(SAFE) Method. In this study, rapid and accurate prediction of the propagation characteristics for guided waves in a wide range of structures has been performed by implementation of SAFE method. Damped and undamped waveguides of different shapes can be modelled. Wave propagation characteristics in both isotropic and anisotropic composite structures can also be studied. To benchmark the solution, a case study using Transfer Matrix Method (TMM) for composite plate has been evaluated. It was found that the element discretizaton plays an important role in accurate prediction of modes in SAFE method, neglecting which leads to loss of higher order modes.

Unsupervised dictionary learning with Fisher discriminant for clustering

This paper presents an advancement in smart sensing and structural health monitoring (SHM) of large-scale ship structures, aimed at real-time detection and accurate localization of damage induced by extreme environmental conditions and high-impact events. This subject has attracted increasing attention in naval architecture, marine, and ocean engineering because such damage has critical implications for structural integrity and safety. In practical applications within harsh marine environments, the capability to rapidly and reliably identify the location of structural damage after an extreme event is essential. To address this need, the proposed approach integrates the inverse finite element method (iFEM), anomaly index formulation, and machine learning (ML) techniques. High-fidelity finite element (FEM) models are employed to simulate damage scenarios with high accuracy; these simulations are then simplified to enable efficient real-time analysis and seamless integration into the SHM framework. The methodology has been applied to a representative case study involving a portion of a containership, effectively overcoming challenges related to optimal sensor placement, environmental variability, and complex operating conditions. Ultimately, the study introduces an enhanced iFEM-based strategy combined with ML models for real-time SHM, providing a robust and scalable solution for damage detection and localization in large-scale ship structures under extreme conditions. • Enhanced real-time monitoring and damage detection via advanced sensors integrated with numerical models. • Seamless integration of iFEM, Anomaly Index, Deep Neural Networks, and computational methods. • Use of high-fidelity numerical models for impact damage simulation. • Implementation on a real marine structure, demonstrating effectiveness in practical applications.

Guided wave-based damage evaluation has been regarded as a promising method in the area of structural health monitoring. The main obstacle for the practical application of these guided wave-based monitoring methods is the reliability of damage evaluation under time-varying ambient conditions. In this paper, an analytical model and a semi-analytical finite element (SAFE) method are proposed to study the effect of temperature and load on guided wave propagation in an isotropic plate respectively including the dispersion curves and waveform. In the presented models, the temperature and load dependent elastic constants are considered to study the variations of guided wave properties. The result shows that the phase velocity gradually decreases with the incremental temperature. It is also observed that the phase velocity gradually decreases with the incremental load. Finally, the analytical model and SAFE method are validated through the experimental data. It shows that the results obtained from the theoretical model match well with the experimental results.

Thermal protection systems (TPSs) are essential to protect reusable hypersonic vehicles from harsh aerothermal environments. This paper investigates guided wave dispersion in TPS using semi-analytical finite element (SAFE) method for further non-destructive testing of the inter-laminar debonding. A theoretical model is developed to describe mode coupling of guided waves between the load-bearing substrate and thermal insulation material. SAFE method is then utilized to obtain 3-D dispersion curves of guided wave modes in typical TPS. Due to the material uncertainty, different damping situations of the thermal insulation material are considered in numerical simulation. Compared with the wavenumber loci of guided wave modes in the load-bearing substrate, those in the intact TPS vary dramatically around the critical frequency due to the coupling effect of the bonded thermal insulation material. Coupling regions of multiple guided wave modes are found under different damping situations. The results show that guided wave modes around the critical frequency are suitable for the evaluation of bonding condition between the load-bearing substrate and thermal insulation material. Overall, the dispersion and attenuation property of guided waves in typical TPS are analyzed. The proposed characterization method provides theoretical support for TPS non-destructive testing using laser-generated guided waves.

Chapter 8 - Guided-wave excitation in aerospace composites

SAFE method for dispersion characteristics of fluid-saturated porous media with arbitrary cross sections.