Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

A note on the inverse mode shape problem for bars, beams, and plates

Motivated by the idea of designing a structure for a desired mode shape, intended towards applications such as resonant sensors, actuators and vibration confinement, we present the inverse mode shape problem for bars, beams and plates in this work. The objective is to determine the cross-sectional profile of these structures, given a mode shape, boundary condition and the mass. The contribution of this article is twofold: (i) A numerical method to solve this problem when a valid mode shape is provided in the finite element framework for both linear and nonlinear versions of the problem. (ii) An analytical result to prove the uniqueness and existence of the solution in the case of bars. This article also highlights a very important question of the validity of a mode shape for any structure of given boundary conditions.

A mode-shape classification technique for robust speech rate estimation and syllable nuclei detection

Acoustic feature based speech (syllable) rate estimation and syllable nuclei detection are important problems in automatic speech recognition (ASR), computer assisted language learning (CALL) and fluency analysis. A typical solution for both the problems consists of two stages. The first stage involves computing a short-time feature contour such that most of the peaks of the contour correspond to the syllabic nuclei. In the second stage, the peaks corresponding to the syllable nuclei are detected. In this work, instead of the peak detection, we perform a mode-shape classification, which is formulated as a supervised binary classification problem - mode-shapes representing the syllabic nuclei as one class and remaining as the other. We use the temporal correlation and selected sub-band correlation (TCSSBC) feature contour and the mode-shapes in the TCSSBC feature contour are converted into a set of feature vectors using an interpolation technique. A support vector machine classifier is used for the classification. Experiments are performed separately using Switchboard, TIMIT and CTIMIT corpora in a five-fold cross validation setup. The average correlation coefficients for the syllable rate estimation turn out to be 0.6761, 0.6928 and 0.3604 for three corpora respectively, which outperform those obtained by the best of the existing peak detection techniques. Similarly, the average F-scores (syllable level) for the syllable nuclei detection are 0.8917, 0.8200 and 0.7637 for three corpora respectively. (C) 2016 Elsevier B.V. All rights reserved.

Mode shape expansion using perturbed force vector approach

A new technique for mode shape expansion in structural dynamic applications is presented based on the perturbed force vector approach. The proposed technique can directly adopt the measured incomplete modal data and include the effect of the perturbation between the analytical and test models. The results show that the proposed technique can provide very accurate expanded mode shapes, especially in cases when significant modelling error exists in the analytical model and limited measurements are available.

DEVELOPMENT OF AN IONIC LIQUID FERROFLUID ELECTROSPRAY SOURCE AND MODE SHAPE STUDIES OF A FERROFLUID IN A NON-UNIFORM MAGNETIC FIELD

An electrospray source has been developed using a novel new fluid that is both magnetic and conductive. Unlike conventional electrospray sources that required microfabricated structures to support the fluid to be electrosprayed, this new electrospray fluid utilizes the Rosensweig instability to create the structures in the magnetic fluid when an external magnetic field was applied. Application of an external electric field caused these magnetic fluid structures to spray. These fluid based structures were found to spray at a lower onset voltage than was predicted for electrospray sources with solid structures of similar geometry. These fluid based structures were also found to be resilient to damage, unlike the solid structures found in traditional electrospray sources. Further, experimental studies of magnetic fluids in non-uniform magnetic fields were conducted. The modes of Rosensweig instabilities have been studied in-depth when created by uniform magnetic fields, but little to no studies have been performed on Rosensweig instabilities formed due to non-uniform magnetic fields. The measured spacing of the cone-like structures of ferrofluid, in a non-uniform magnetic field, were found to agree with a proposed theoretical model.

Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials

Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup. (C) 2013 Elsevier B.V. All rights reserved.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Capturing mode-switching in postbuckling composite panels using a modified explicit procedure

A postbuckling blade-stiffened composite panel was loaded in uniaxial compression, until failure. During loading beyond initial buckling, this panel was observed to undergo a secondary instability characterised by a dynamic mode shape change. These abrupt changes cause considerable numerical difficulties using standard path-following quasi-static solution procedures in finite element analysis. Improved methods such as the arc-length-related procedures do better at traversing certain critical points along an equilibrium path but these procedures may also encounter difficulties in highly non-linear problems. This paper presents a robust, modified explicit dynamic analysis for the modelling of postbuckling structures. This method was shown to predict the mode-switch with good accuracy and is more efficient than standard explicit dynamic analysis. (C) 2003 Elsevier Science Ltd. All rights reserved.

Buckling mode transition in hat-stiffened composite panels loaded in uniaxial compression

A combined experimental and analytical study of a hat-stiffened carbon-fibre composite panel loaded in uniaxial compression was investigated. A buckling mode transition was observed in the panel's skin bay which was not captured using non-linear finite-element analysis. Good correlation between experimental and numerical strain and displacement results was achieved in the prebuckling and initial postbuckling region of the loading history. A Marguerre-type Rayleigh-Ritz energy method was applied to the skin bay using representative displacement functions of permissible mode shapes to explain the mode transition phenomenon. The central criterion of this method was based on the assumption that a change in mode shape occurred such that the total potential energy of the structure was maintained at a minimum. The ultimate strength of the panel was limited by the column buckling strength of the hat-stiffeners.

Damage assessment in structures using vibration characteristics

Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage in structures, especially in bridges, which are designed for long life spans. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting in order to avoid failure or collapse of the structures. In recent times, structural health monitoring (SHM) has attracted much attention in both research and development. Local and global methods of damage assessment using the monitored information are an integral part of SHM techniques. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localization of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based methods, which give a global damage assessment. The vibration-based damage detection methods use measured changes in dynamic characteristics to evaluate changes in physical properties that may indicate structural damage or degradation. The basic idea is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Changes in the physical properties will therefore cause changes in the modal properties. Any reduction in structural stiffness and increase in damping in the structure may indicate structural damage. This research uses the variations in vibration parameters to develop a multi-criteria method for damage assessment. It incorporates the changes in natural frequencies, modal flexibility and modal strain energy to locate damage in the main load bearing elements in bridge structures such as beams, slabs and trusses and simple bridges involving these elements. Dynamic computer simulation techniques are used to develop and apply the multi-criteria procedure under different damage scenarios. The effectiveness of the procedure is demonstrated through numerical examples. Results show that the proposed method incorporating modal flexibility and modal strain energy changes is competent in damage assessment in the structures treated herein.

Evaluation of modal analysis techniques using physical models to detect osseointegration of implants in transfemoral amputees

Non-invasive vibration analysis has been used extensively to monitor the progression of dental implant healing and stabilization. It is now being considered as a method to monitor femoral implants in transfemoral amputees. This paper evaluates two modal analysis excitation methods and investigates their capabilities in detecting changes at the interface between the implant and the bone that occur during osseointegration. Excitation of bone-implant physical models with the electromagnetic shaker provided higher coherence values and a greater number of modes over the same frequency range when compared to the impact hammer. Differences were detected in the natural frequencies and fundamental mode shape of the model when the fit of the implant was altered in the bone. The ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

An improved method to detect damage using modal strain energy based damage index

This paper presents two novel concepts to enhance the accuracy of damage detection using the Modal Strain Energy based Damage Index (MSEDI) with the presence of noise in the mode shape data. Firstly, the paper presents a sequential curve fitting technique that reduces the effect of noise on the calculation process of the MSEDI, more effectively than the two commonly used curve fitting techniques; namely, polynomial and Fourier’s series. Secondly, a probability based Generalized Damage Localization Index (GDLI) is proposed as a viable improvement to the damage detection process. The study uses a validated ABAQUS finite-element model of a reinforced concrete beam to obtain mode shape data in the undamaged and damaged states. Noise is simulated by adding three levels of random noise (1%, 3%, and 5%) to the mode shape data. Results show that damage detection is enhanced with increased number of modes and samples used with the GDLI.

Correlation-based damage detection for complicated truss bridges using multi-layer genetic algorithms

The study presents a multi-layer genetic algorithm (GA) approach using correlation-based methods to facilitate damage determination for through-truss bridge structures. To begin, the structure’s damage-suspicious elements are divided into several groups. In the first GA layer, the damage is initially optimised for all groups using correlation objective function. In the second layer, the groups are combined to larger groups and the optimisation starts over at the normalised point of the first layer result. Then the identification process repeats until reaching the final layer where one group includes all structural elements and only minor optimisations are required to fine tune the final result. Several damage scenarios on a complicated through-truss bridge example are nominated to address the proposed approach’s effectiveness. Structural modal strain energy has been employed as the variable vector in the correlation function for damage determination. Simulations and comparison with the traditional single-layer optimisation shows that the proposed approach is efficient and feasible for complicated truss bridge structures when the measurement noise is taken into account.

Innovative damage assessment of steel truss bridges using modal strain energy correlation

As a part of vital infrastructure and transportation network, bridge structures must function safely at all times. Bridges are designed to have a long life span. At any point in time, however, some bridges are aged. The ageing of bridge structures, given the rapidly growing demand of heavy and fast inter-city passages and continuous increase of freight transportation, would require diligence on bridge owners to ensure that the infrastructure is healthy at reasonable cost. In recent decades, a new technique, structural health monitoring (SHM), has emerged to meet this challenge. In this new engineering discipline, structural modal identification and damage detection have formed a vital component. Witnessed by an increasing number of publications is that the change in vibration characteristics is widely and deeply investigated to assess structural damage. Although a number of publications have addressed the feasibility of various methods through experimental verifications, few of them have focused on steel truss bridges. Finding a feasible vibration-based damage indicator for steel truss bridges and solving the difficulties in practical modal identification to support damage detection motivated this research project. This research was to derive an innovative method to assess structural damage in steel truss bridges. First, it proposed a new damage indicator that relies on optimising the correlation between theoretical and measured modal strain energy. The optimisation is powered by a newly proposed multilayer genetic algorithm. In addition, a selection criterion for damage-sensitive modes has been studied to achieve more efficient and accurate damage detection results. Second, in order to support the proposed damage indicator, the research studied the applications of two state-of-the-art modal identification techniques by considering some practical difficulties: the limited instrumentation, the influence of environmental noise, the difficulties in finite element model updating, and the data selection problem in the output-only modal identification methods. The numerical (by a planer truss model) and experimental (by a laboratory through truss bridge) verifications have proved the effectiveness and feasibility of the proposed damage detection scheme. The modal strain energy-based indicator was found to be sensitive to the damage in steel truss bridges with incomplete measurement. It has shown the damage indicator's potential in practical applications of steel truss bridges. Lastly, the achievement and limitation of this study, and lessons learnt from the modal analysis have been summarised.