FRF-based damage localization method with noise suppression approach

In this paper a noise-robust damage identification method is presented for localization of structural damage in presence of heavy noise influences. The method works based on Frequency Response Functions (FRFs) of the damaged structure without any prior knowledge of the healthy state. The main innovation of this study starts with convolving FRFs with Gaussian kernel to suppress the noise. Denoised signals are then used to develop shape signals according to the second derivative of the operational mode shapes at frequencies in the half-power bandwidth of the center resonant frequencies. The scheme is followed by normalization of shape signals to create a two-dimensional map indicating the damage pattern. The validation of the method was carried out based on simulated data and experimental measurements. The simulated data polluted with 10 percent random noise considering four different conditions: (i) un-correlated noise with Gaussian distribution (ii) noise with non-Gaussian exponential distribution (iii) noise with non-Gaussian Log-normal distribution and (iv) correlated colored noise. The robustness of the method was examined with respect to the damage severity with various damage conditions. Finally, damage detection experiments of a fixed–fixed steel beam are presented to illustrate the feasibility and effectiveness of the proposed method. According to the numerical and experimental investigations, it was demonstrated that the proposed approach presents satisfactory damage indices both in single and multiple damage states in presence of high level noise. Hence, the method can overcome the problems of output measurement noise and deliver encouraging results on damage localization.     

Structural damage detection using cross correlation functions of vibration response

Structural damage detection methods based on vibration responses are appealing for a variety of reasons such as their potential to observe damage from sensors placed remote from an unknown damage site. Of particular interest to the authors is online damage detection in which changes in the structure can be flagged up in an automated fashion by permanently installed transducers. In a previous paper by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between response measurements. Implicitly assumed in the formulation is that the response quantity is that of displacement resulting from white noise excitation. In this paper, the IPV technique is first reviewed and then generalised to address velocity and acceleration response to band pass white noise excitation. It is shown that the IPV is a weighted summation of the mode shapes, and the effect of some particular measurement noise on the IPV can be adaptively eliminated in the calculation of IPV. Then, the damage detection method based on changes in the IPV is proposed. Finally, damage detection experiments of shear frame structure, honeycomb sandwich composite beam and aircraft stiffened panel are presented to illustrate the feasibility and effectiveness of the proposed method.     

Mode shape expansion using perturbed force approach

A new approach for expanding incomplete experimental mode shapes is presented which considers the modelling errors in the analytical model and the uncertainties in the vibration modal data measurements. The proposed approach adopts the perturbed force vector that includes the effect of the discrepancy in mass and stiffness between the finite element model and the actual tested dynamic system. From the developed formulations, the perturbed force vector can be obtained from measured modal data and is then used for predicting the unmeasured components of the expanded experimental mode shapes. A special case that does not require the experimental natural frequency in the mode shape expansion process is also discussed. A regularization algorithm based on the Tikhonov solution incorporating the generalized cross-validation method is employed to filter out the influence of noise in measured modal data on the predictions of unmeasured mode components. The accuracy and robustness of the proposed approach is verified with respect to the size of measured data set, sensor location, model deficiency and measurement uncertainty. The results from two numerical examples, a plane frame structure and a thin plate structure, show that the proposed approach has the best performance compared with the commonly used existing expansion methods, and can reliably produce the predictions of mode shape expansion, even in the cases with limited modal data measurements, large modelling errors and severe measurement noise.     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

Damage identification for beams in noisy conditions based on Teager energy operator-wavelet transform modal curvature

Modal curvatures have been widely used in the detection of structural damage. Attractive features of modal curvature include great sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency in a modal curvature is its susceptibility to the measurement noise present in the displacement mode shape that produces the modal curvature, likely obscuring the features of damage. To address this deficiency, the Teager energy operator together with wavelet transform is tactically utilized to treat modal curvature, producing a new modal curvature, termed the Teager energy operator-wavelet transform modal curvature. This new modal curvature features distinct capabilities of suppressing noise, canceling global trends, and intensifying the singular feature caused by damage for a measured mode shape involving noise. These features maximize the sensitivity to damage and accuracy of damage localization. The proposed modal curvature is demonstrated in several analytical cases of cracked pinned–pinned, clamped–free and clamped–clamped beams, with emphasis on characterizing damage in noisy conditions, and it is further validated by an experimental program using a scanning laser vibrometer to acquire mode shapes of a cracked aluminum beam. The Teager energy operator-wavelet transform modal curvature essentially overcomes the deficiency of conventional modal curvature, providing a new dynamic feature well suited for damage characterization in noisy environments. (The Matlab code for implementing Teager energy operator-wavelet transform modal curvature can be provided by the corresponding author on request.)     

Singular spectrum analysis for enhancing the sensitivity in structural damage detection

Time domain structural condition assessment methods have been studied extensively in the last two decades due to their effectiveness in dealing with limited and short duration measurements from a structure under operational conditions. The sensitivity-based method is revisited in this paper with an enhancement in the sensitivity with respect to local damages via the singular spectrum analysis technique. The measured response of the structure is decomposed and the sensitivity vectors as well as the computed response vectors are projected into the corresponding decomposition subspace. The projected identification equations associate with components which contain the least measurement noise and the most damage information are then used to detect local damages in the structure. The enhanced sensitivity-based method is shown to be capable of yielding more accurate identified results with noisy measurement in a planar truss structure compared to conventional sensitivity-based method. A seven-storey steel frame test is performed in the laboratory, and the proposed method is checked to be able to identify the damage location and extend of this structure with an acceptable accuracy.     

Identification of structural systems with full characteristic matrices under single point excitation

The aim of “System Identification” is to determine modal and system properties of structural systems. This is while in “Damage Detection”, the identification of system characteristic matrices is as important as or even more important than the identification of frequency characteristics. Because of various constraints – i.e. difficulties in force excitation of structures due to their large size, geometry, and location – in practice only single excitation and partial measurement, at selected degrees of freedom, is possible. In this paper, a single dynamic load was applied to identify a structural system only along one of the degrees of freedom of the structure. Further, responses corresponding to a few degrees of freedom were also measured. To identify a system with this sort of restricted information, a new approach was introduced enabling identification of the structure?s parameters of mass, damping and stiffness. Taking into account the significant effect of noise reduction in improving system identification accuracy levels, a noise reduction technique was also proposed. The accuracy of the method was also assessed against noise level and location of single excitation. It was shown that as noise level increases, identification errors will also increase (less than 3.5 percent). It was further observed that applying single force at the first storey of the flexural structure would yield the lowest error levels in the identification results. Later, the method?s efficiency and precision were examined through the application of a “closed loop solution” to a six-storey flexural structure, and a four-span Pratt truss. The obtained results showed that the proposed method could act as an effective model in identification of system properties.     

Damage localisation in plate like-structures using the two-dimensional polynomial annihilation edge detection method

The topic of non-destructively detecting localised damage in plates is addressed in this article. Since the presence of a crack or a delamination causes a discontinuity in the mode shape first derivatives, a numerical method for detecting discontinuities in smooth piecewise functions and their derivatives, based on a polynomial-annihilation technique is presented. The method, already proposed for beam-type structures, has been extended to enable the detection and localisation of damage in plate-like structures for which only post-damage mode shapes are available. Applying finite element analysis, the mode shapes of an isotropic plate with a saw-cut and a multi-layered composite plate with a delamination have been calculated and the performance of the approach evaluated for increasing amounts of noise. Encouraging results indicate that further development of the technique for non-destructive testing of plate-like structures would be highly worthwhile.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

Improved damage detection method based on Element Modal Strain Damage Index using sparse measurement

An improved damage detection method based on the concept of Element Modal Strain Damage Index is introduced. The proposed methods attempts to address some of the weaknesses of the damage detection method based on modal curvatures. The use of numerical differentiation procedures is identified as the main cause for the poor performance of the modal curvature method under sparse and noisy measurement. An improved damage index that does not rely on numerical differentiation is then formulated. The proposed damage index can be calculated using only modal displacement and modal rotation. A penalty-based minimization approach is then used to find the unknown modal rotation using sparse and noisy modal displacement measurement. Numerical simulation and experiment validation confirm the relative advantage of the proposed method compared with modal curvature-based approaches.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

Acoustic-based damage detection method

Most of the structural health monitoring (SHM) methods is either based on vibration-based and contact acoustic emission (AE) techniques. Both vibration-based and acoustic emission techniques require attaching transducers to structure. In many applications, such as those involving hot structural materials for thermal protection purposes or in rotating machines, non-contact measurements would be preferred because the operating environment is prohibitive leading to potential damage in contact sensors or their attachments. In this paper, a new non-contact, acoustic-based damage detection method is proposed and tested with an objective that the proposed method is able to detect the location and extend of damage accurately. The proposed acoustic-based damage detection method is a direct method. In this proposed method, changes in vibro-acoustics flexibility matrices of the damage and health structure are used to predict the location and extend of damage in the structure. A case study involving actual measured date for the case of a fixed–fixed plate structure is used to evaluate the effectiveness of the proposed method. The results have shown that the proposed acoustic-based damage detection method can be used to detect the location and extend of the damage accurately.     

On the separation of internal and boundary damage in slender bars using longitudinal vibration frequencies and equivalent linearization of damaged bolted joint response

The problem of detecting localized large-scale internal damage in structures with imperfect bolted joints is considered. The proposed damage detection strategy utilizes the structural damping and an equivalent linearization of the bolted lap joint response to separate the combined boundary damage from localized large-scale internal damage. The frequencies are found approximately using asymptotic analysis and a perturbation technique. The proposed approach is illustrated on an example of longitudinal vibrations in a slender elastic bar with both ends clamped by bolted lap joints with different levels of damage. It is found that while the proposed method allows for the estimation of internal damage severity once the crack location is known, it gives multiple possible crack locations so that other methods (e.g., mode shapes) are required to obtain a unique crack location.     

Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering

This study presents a novel time series analysis methodology to detect, locate, and estimate the extent of the structural changes (e.g. damage). In this methodology, ARX models (Auto-Regressive models with eXogenous input) are created for different sensor clusters by using the free response of the structure. The output of each sensor in a cluster is used as an input to the ARX model to predict the output of the reference channel of that sensor cluster. Two different approaches are used for extracting Damage Features (DFs) from these ARX models. For the first approach, the coefficients of the ARX models are directly used as the DFs. It is shown with a 4 dof numerical model that damage can be identified, located and quantified for simple models and noise free data. To consider the effects of the noise and model complexity, a second approach is presented based on using the ARX model fit ratios as the DFs. The second approach is first applied to the same 4 DOF numerical model and to the numerical data coming from an international benchmark study for noisy conditions. Then, the methodology is applied to the experimental data from a large scale laboratory model. It is shown that the second approach performs successfully for different damage cases to identify and locate the damage using numerical and experimental data. Furthermore, it is observed that the DF level is a good indicator for estimating the extent of the damage for these cases. The potential and advantages of the methodology are discussed along with the analysis results. The limitations of the methodology, recommendations, and future work are also addressed.     

Passive acoustic tomography of the ocean using arrays of unknown shape

It was recently established that ocean acoustic tomography based on an inversion of ray travel times can be implemented without use of any dedicated sound sources by cross-correlating the ambient noise recorded on two line arrays, the shapes of which are known. In contrast to active tomography, the amount of useful information from noise interferometry is proportional to the product of the numbers of receivers in the two arrays. In our study based on the 2D and 3D numerical experiments, we examine a hypothesis concerning the feasibility of simultaneous performance of a passive ray tomography and passive positioning of arrays through cross-correlation of ambient or shipping noise. The numerical experiments are conducted under conditions close to those of a field experiment on passive ocean tomography. It is demonstrated that, when using arrays of 20–40 hydrophones, the sound velocity profile and the array shape can be found from noise correlation to an accuracy adequate for oceanological and acoustic applications.     

Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection

Structural damage detection using time domain vibration responses has advantages such as simplicity in calculation and no requirement of a finite element model, which attracts more and more researchers in recent years. In present paper, a new approach to detect the damage based on the auto correlation function is proposed. The maximum values of the auto correlation function of the vibration response signals from different measurement points are formulated as a vector called Auto Correlation Function at Maximum Point Value Vector, AMV for short. The relative change of the normalized AMV before and after damage is used as the damage index to locate the damage. Sensitivity analysis of the normalized AMV with respect to the local stiffness shows that the normalized AMV has a sharp change around the local stiffness change location, which means the normalized AMV is a good indicator to detect the damage even when the damage is very small. Stiffness reduction detection of a 12-story frame structure is provided to illustrate the validity, effectiveness and the anti-noise ability of the proposed method. Comparison of the normalized AMV and the other correlation-function-based damage detection method shows the normalized AMV has a better detectability.     

Nanomechanical testing of ODS steels irradiated with 1 MeV/amu heavy ions

Development of oxide dispersion strengthened (ODS) steels, as candidates for fuel claddings for Gen IV nuclear reactors, requires a comprehensive study of their behaviour under operating conditions. In this work, 1.2 MeV/amu Kr and Xe irradiation was used to simulate fission fragment impact. New irradiation approaches with respect to a non-homogeneous damage profile under ion irradiation were proposed. Hardness profiles of irradiated ODS steels were obtained by continuous stiffness measurements with subsequent analysis of size effects according to the Nix–Gao model. It was found, that heavy ion irradiation leads to hardness saturation in ODS steels in a damage dose range of 0.1–1 dpa. Observed hardening is about 20% and is not connected with the radiation stability of Y–Ti–O and Y–Al–O oxide particles in ODS steels as it was studied by TEM.     

A frequency shift curve based damage detection method for cylindrical shell structures

A novel damage detection method based on frequency shift curve (FSC) is developed for cylindrical shell structures. The FSC is caused by auxiliary mass containing both the natural frequencies and mode shapes information. According to axis-symmetry, the FSC is flat when there is no damage. However, it shows obvious periodic peaks when localized imperfections or damages occur. Furthermore, for the +2nd FSC, the trough with minimum value indicates the circumferential location of the damage and the difference between the lowest trough value and the values of the other three troughs represents the severity of the local damage. Through changing the location of the accelerometer, which can be considered as an auxiliary mass itself, around the cylindrical shell circumference, the FSCs can be measured and then the damage can be detected and located. Moreover, the difference between the averages of ±2nd FSCs also reflects the severity of damages. Numerical simulation and experimental tests have confirmed the finding. Compared with other vibration based methods, the proposed method is fast, sensitive and feasible to implement in practice as the measured frequency is more accurate than the mode shapes, and only a single accelerometer is required in the tests.     

A NUMERICAL STUDY OF STRUCTURAL DAMAGE DETECTION USING CHANGES IN THE ROTATION OF MODE SHAPES

Damage detection using changes in global dynamic characteristics has been a hot research topic and attracted civil, aerospace, and mechanical engineering communities in recent years. In this paper, a numerical study of the relationship between damage characteristics and the changes in the dynamic properties is presented. It is found that the rotation of mode shape is a sensitive indicator of damage. The numerical results clarify that the rotation of mode shape has the characteristic of localization at the damaged region even though the displacement modes are not localized. Also, the results illustrate that the rotations of modes are robust in locating multiple damage locations with different sizes in a structure. Furthermore, using the changes in the rotation of mode shape does not need very fine grid of measurements to detect and locate damage, effectively.     

Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy

Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very helpful for the daily inspection or maintenance of civil structures. Although entropy analysis has shown excellent accuracy, it still consumes too much time and too many resources in terms of data processing. To improve the dilemma, in this study, modified multi-scale symbolic dynamic entropy (MMSDE) is adopted to identify the damaged location of the civil structure. A damage index (DI) based on the entropy diagram is also proposed to clearly indicate the damage location. A seven-story numerical model was created to verify the efficiency of the proposed SHM system. The results of the analysis of each case of damage show that the MMSDE curve for the damaged floor is lower than that for the healthy floor, and the structural damage can be correctly diagnosed by the damage index. Subsequently, a scaled-down steel benchmark experiment, including 15 damage cases, was conducted to verify the practical performance of the SHM system. The confusion matrix was used to further evaluate the SHM system. The results demonstrated that the MMSD-based system can quickly diagnose structural safety with reliability and accuracy. It can be used in the field of long-term structural health monitoring in the near future.