Computational Techniques for Structural Health Monitoring

This chapter presents an introduction to Structural Health Monitoring (SHM), by defining the terminology, summarizing the most common techniques, and identifying outstanding research issues. The essential components of an SHM system are also outlined to highlight the important role of numerical simulations in SHM, which is the fundamental theme of this book. The chapter ends with a summary of the organization and contents of the book in order to guide the readers through its various parts.

This chapter provides an overview of fundamental concepts in elasticity and structural mechanics which will support the understanding of the material presented in the later chapters. The topics covered include basics of elasticity, mechanics of composites, beam and plate theories, and wave propagation.

Structural health monitoring heavily relies on signal processing techniques that are necessary to post-process measured signals. It is these signals that indicate the state of the structure. This chapter addresses some of the important issues regarding signal processing of the measured signals, as it applies to the detection and characterization of damage.

This chapter presents some of the aspects in the application of the finite element method (FEM) for structural health monitoring (SHM) problems. First, the procedure to select a proper FE mesh size for a given frequency content of a predefined input is given. A relationship between the damage size and the frequency of the predefined input signal is then established. Different methods of modeling flaws in FEM and their utility in SHM studies are explained through numerical examples. Limitations of FEM for SHM and possible remedies are also discussed.

This chapter presents the procedures for the development of various types of spectral elements. The chapter begins with basic outline of spectral finite element formulation and illustrates its utility for wave propagation studies is complex structural components. Two variants of spectral formulations, namely the Fourier transform-based, and Wavelet transform-based spectral FEM are presented for both 1D and 2D waveguides. A number of examples are solved using the formulated elements to show the effectiveness of the spectral FEM approach to solve problems involving high frequency dynamic response.

This chapter presents several spectral element models for damaged waveguides. Models are developed for horizontal through-width single and multiple cracks (or delaminations), vertical through-width cracks (fiber breakages) and surface breaking cracks in 1D waveguides and vertical through-width cracks in 2D waveguides are addressed. Wave scattering due to these damage types are investigated with particular focus on composite structures. Examples shown in this chapter use both spectral element formulations previously presented, namely the FSFEM and WSFEM.

In this chapter, analysis methods for notch type and line type defects are presented, which are based on perturbation techniques. The line defect could be a horizontal crack (through width delamination) or through width vertical crack (fiber breaks). Modeling of some of these defects were addressed in the last chapter and the methods presented here represent another approach to the simplified modeling of these defects.

The analysis of wave propagation has been extensively used as a tool for non destructive evaluation of structural components. The numerical analysis of wavefield in damaged media can be useful to investigate the problem theoretically and to support the interpretation of experimental measurements. A finite element analysis of non homogeneous media can be computationally very expensive, especially when a fine mesh is required to properly model the geometric and/or material discontinuities that are characteristic of the damaged areas. The computational cost associated with wave propagation simulations motivates the development of the simplified damage models presented in Chaps.​ 6 and 7. This chapter presents a different approach whereby the computational cost is reduced through a multi-scale analysis. A coarse mesh is employed to capture the macroscopic behavior of the structure, and a refined mesh is limited to the small region around the discontinuity. The co-existence of two scales in the model is handled through the application of proper bridging relations between the two scales, and the generation of interaction forces at the interfaces according to the Bridging Scales Method. This technique allows a coarse description of the global behavior of the structure while simultaneously obtaining local information regarding the interaction of propagating waves with a localized discontinuity in the domain. Time and frequency domain formulations of the Bridging Scales Method are illustrated through examples on simulations of 1D and 2D waveguides.

This chapter presents computational techniques for the simulation of guided wave generation in plate structures. Generation is here considered as achieved by surface mounted piezoelectric patches of various shapes and characteristics. This computationally costly task is performed through the application of semi-analytical techniques, which involve the solution of the governing elasto-dynamic equations in the frequency/wavenumber domain, and the evaluation of the structure (plate) response in the far-field. Such techniques are presented and further extended to illustrate their joint application with the Finite Element solution of the interface stress between a surface mounted patch and the structural substrate. These methodologies are subsequently applied for the analysis of directional wave generation through actuator arrays. The concept of beam steering through phase control of the array elements, and through their spatial arrangement is presented for the simple case of a linear, one-dimensional array. The basic principles are then applied to the case of a two-dimensional configuration which has the ability to generate beam steering through proper tuning of the excitation frequency. The concept of “frequency-based" steering is discussed in detail as an effective and efficient means for directional wave generation and for focusing of the acoustic energy. The chapter ends with the presentation of methodologies for wave sensing. Most of the presented procedures illustrate the reciprocity between sensing and actuation, along with the opportunity for optimal sensing/generation through proper shaping and/or spatial distribution of the patch elements.

This chapter presents an overview of techniques used to analyze the dynamic response of structures with the objective of detecting, locating and quantifying structural damage. A quick summary of vibration-based techniques is first provided as an introduction to the strainᾢenergy ratio technique. The ability of the strain energy ratio to locate damage and potentially estimate its severity is illustrated through numerical simulations and experimental results on beams and plates. The extension of the concept to the analysis of the wave propagation response is also presented to demonstrate the generality of the approach. Wave-based techniques for the detection and quantification of damage also include the phase gradient technique, and the mode conversion estimation, which are also presented. The chapter concludes with the detailed presentation of the damage force indicator technique as yet another method for damage localization.

This chapter gives an overview on the use of soft computing tools for damage detection in SHM. Here, two important soft computing tools, namely the genetic algorithms and the artificial neural network are addressed in regard to damage detection. Implementation of these methods under spectral finite element environment is discussed. The chapter first gives basic introduction to these methods and outlines the procedure for adaptation under spectral FEM environment. A number of examples are given to show the effectiveness of these methods for damage detection.