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About this book

This book discusses systems of damage detection and structural health monitoring in mechanical, civil, and aerospace structures. It utilizes principles of fuzzy logic, probability theory, and signal processing to develop systems and approaches that are robust in the presence of both noise in the data and variations in properties of materials which are intrinsic to the process of mass production. This volume will be useful to graduate students, researchers, and engineers working in this area, especially those looking to understand and address model uncertainty in their algorithms.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
Structures are prone to degradation and damage over their service life. Damage detection is one of the main aspects of structural engineering both for safety reasons and because of economic benefits that can result from the prevention of failure. Many nondestructive testing methods for structural health monitoring have been proposed over the past few decades.
Ranjan Ganguli

Chapter 2. Fuzzy Logic and Probability in Damage Detection

Abstract
A simple application problem is selected to illustrate key concepts of uncertainty modeling, probabilistic analysis, and fuzzy logic in the context of damage detection. The problem involves local damage in a cantilever beam with natural frequency damage indicators. The modeling aspects of the problem are kept simple to allow the development of algorithmic concepts. The governing equation of a Euler–Bernoulli beam is presented in Sect. 2.1.
Ranjan Ganguli

Chapter 3. Modal Curvature Based Damage Detection

Abstract
In the present chapter, a finite element model of a cantilever beam is used to develop a fuzzy logic system (FLS) for damage detection in structures using modal curvature vectors. A new sliding window defuzzifier proposed for fault isolation in Chap. 2 for frequency damage indicators is now extended to modal curvature. The proposed FLS is tested for noisy data as well as for the case when some of the measurements are missing or faulty. Section 3.1 provides a background on modal methods for damage detection and motivates the use of modal curvature as a damage indicator. Section 3.2 presents the beam model and defines the mode shape curvature. Section 3.3 presents the fuzzy logic system based on inputs from modal curvatures and outputs involving damage size and location. Section 3.4 presents damage detection results using modal curvature for the case where no material uncertainty is present. Section 3.5 then moves from a uniform beam model to a tapered beam model and considers multiple damages in the beam. Section 3.6 introduces the curvature damage factor as an indicator of damage. Section 3.7 presents the material uncertainty model for the isotropic steel tapered beam and Sect. 3.8 discusses the uncertainty quantification method. Section 3.9 presents a fuzzy logic system for the uncertain tapered beam and Sect. 3.10 presents damage detection results. Finally, Sect. 3.10 presents the main ideas from the chapter. The content of this chapter is adapted from [1, 2].
Ranjan Ganguli

Chapter 4. Damage Detection in Composite Plates

Abstract
The previous two chapters introduced the problem of damage detection in isotropic steel beams. In this chapter, we advance the problem in terms of realism and complexity by considering a plate structure made of composite material. Composite materials have created a huge impact on structural engineering in the aerospace, automobile, civil, or mechanical industry, due to their superior fatigue characteristics and high specific structural properties as compared to that of metals. But they are also very susceptible to damage caused by low- or high-velocity impacts which can result in delamination between composite layers. This can adversely affect structural life and safety aspects.
Ranjan Ganguli

Chapter 5. Damage Detection in Smart Composite Plates

Abstract
In this chapter, a damage detection approach for a smart composite structure is presented. A brief background on smart structures is provided in Sect. 5.1. Smart structural systems have gained importance in recent years and have found applications in aerospace, automotive, and space applications [14]. A structure can be made smart by introducing sensors, actuators, and information processing algorithms.
Ranjan Ganguli

Chapter 6. Damage Growth Monitoring in Composite Plates

Abstract
Composites play an important role in modern industry, especially in aerospace structures because of their high specific strength and specific stiffness values [1]. Structural health monitoring of composites is, therefore, an important area of current research [2]. This chapter investigates the detection of matrix cracks and delamination in composite plates while adding material uncertainty. Section 6.1 presents background literature to motivate this chapter. Section 6.2 presents the composite plate model and the matrix crack model. Section 6.3 validates these models with published work. Section 6.4 presents numerical results for deflection and frequency for damaged plates while accounting for uncertainty. Section 6.5 presents the delamination model. Section 6.5 shows the results of matrix crack saturation and delamination on the composite plate system properties and evaluates the suitability of these damage indicators for uncertainty quantification. Finally, Sect. 6.7 presents the summary of this chapter. The content of this chapter is adapted from [3] and [4].
Ranjan Ganguli

Chapter 7. Wavelet Based Damage Detection

Abstract
In this chapter, a wavelet-based matrix crack detection of a composite structure is presented. Local matrix crack detection is considered. Section 7.1 presents background material for the published literature to motivate this chapter. Section 7.2 presents an introduction to the wavelet transform, the damage model and finite element analysis method for the composite beam. Section 7.3 presents numerical results for wavelet-based damage detection of the beam structure while accounting for uncertainty in material and measurement. Finally, Sect. 7.4 presents a summary of this chapter. The content of this chapter is adapted from [1].
Ranjan Ganguli

Chapter 8. Fractal Dimension Based Damage Detection

Abstract
This chapter presents a fractal dimension approach to damage detection in composite structures. This approach provides an alternative to the wavelet approach in the previous chapter and is model free. This means that the fractal approach can be used directly with measured data. We also use a static deflection profile in this chapter as a response variable. The deflection profile can be sensitive to local damage, as we shall show in this chapter. Matrix cracks are considered as a local damage and spatial variation in material properties is considered. Section 8.1 presents some background from the literature to motivate the use of fractal dimension measure in structural damage detection. Section 8.2 presents the definition of fractal dimension and an outline of the composite plate model with matrix cracks. Section 8.3 presents numerical results of composite plate static deflection and the effect of curvature, fractal dimension operator and the curvature of fractal dimension on the static deflection of a plate with a seeded local damage. Uncertainty in the material properties is introduced as a random field. Section 8.4 presents a summary of this chapter. This chapter is based on material in [1].
Ranjan Ganguli
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