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.)     

A local flexibility method for vibration-based damage localization and quantification

A method for vibration-based damage localization and quantification, based on quasi-static flexibility, is presented. The experimentally determined flexibility matrix is combined with a virtual load that causes nonzero stresses in a small part of the structure, where a possible local stiffness change is investigated. It is shown that, if the strain–stress relationship for the load is proportional, the ratio of some combination of deformations before and after a stiffness change has occurred, equals the inverse local stiffness ratio. The method is therefore called local flexibility (LF) method. Since the quasi-static flexibility matrix can be composed directly from modal parameters, the LF method allows to determine local stiffness variations directly from measured modal parameters, even if they are determined from output-only data. Although the LF method is in principle generally applicable, the emphasis in this paper is on beam structures. The method is validated with simulation examples of damaged isostatic and hyperstatic beams, and experiments involving a reinforced concrete free–free beam and a three-span prestressed concrete bridge, that are both subjected to a progressive damage test.     

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.     

Condition assessment of reinforced concrete beams using dynamic data measured with distributed long-gage macro-strain sensors

A new condition assessment strategy of reinforced concrete (RC) beams is proposed in this paper. This strategy is based on frequency analysis of the dynamic data measured with distributed long-gage macro-stain sensors. After extracting modal macro-strain, the reference-based damage index is theoretically deducted in which the variations of modal flexural rigidity and modal neutral axis height are considered. The reference-free damage index is also presented for comparison. Both finite element simulation and experiment investigations were carried out to verify the proposed method. The manufacturing procedure of long-gage fiber Bragg grating (FBG) sensor chosen in the experiment is firstly presented, followed by an experimental study on the essential sensing properties of the long-gage macro-strain sensors and the results verify the excellent sensing properties, in particular the measurement accuracy and dynamic measuring capacity. Modal analysis results of a concrete beam show that the damage appearing in the beam can be well identified by the damage index while the vibration testing results of a RC beam show that the proposed method can not only capture small crack initiation but its propagation. It can be concluded that distributed long-gage dynamic macro-strain sensing technique has great potential for the condition assessment of RC structures subjected to dynamic loading.     

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.     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

CRACK DETECTION IN BEAM-TYPE STRUCTURES USING FREQUENCY DATA

A practical method to non-destructively locate and estimate size of a crack by using changes in natural frequencies of a structure is presented. First, a crack detection algorithm to locate and size cracks in beam-type structures using a few natural frequencies is outlined. A crack location model and a crack size model are formulated by relating fractional changes in modal energy to changes in natural frequencies due to damage such as cracks or other geometrical changes. Next, the feasibility and practicality of the crack detection scheme are evaluated for several damage scenarios by locating and sizing cracks in test beams for which a few natural frequencies are available. By applying the approach to the test beams, it is observed that crack can be confidently located with a relatively small localization error. It is also observed that crack size can be estimated with a relatively small size error.     

AN INTELLIGENT TAP TEST AS AN INSPECTION TOOL FOR CORROSION IN CHEQUER PLATE FLOORS

The “coin-tap” test has the ability to indicate damage in a structural element due to a localized change of stiffness or damping. The change in vibration signature may be detected by ear or more precisely by measurement of the dynamic contact force. A method for discriminating between measurements made on sound and damaged structures is presented. An unsupervised neural network algorithm is used for recognizing the differences between contact force patterns. The method is used for non-destructive inspection of corrosion damage to steel chequer plate floors in industrial buildings. It is shown that the intelligent tap test is a useful and practical diagnostic tool for detecting localized damage in structures.     

Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.     

IMPROVED DAMAGE IDENTIFICATION METHOD BASED ON MODAL INFORMATION

In this paper, a newly derived algorithm to predict locations and severities of damage in structures using changes in modal characteristics is presented. First, two existing algorithms of damage detection are reviewed and the new algorithm is formulated in order to improve the accuracy of damage localization and severity estimation by eliminating erratic assumptions and limits in the existing algorithms. Next, the damage prediction accuracy is numerically assessed for each algorithm when applied to a two-span continuous beam for which pre- and post-damage modal parameters are available for only a few modes of vibration. Compared to the existing damage detection algorithms, the new algorithm improved the accuracy of damage localization and severity estimation results in the test beam.     

High sensitive and large dynamic range quasi-distributed sensing system based on slow-light π-phase-shifted fiber Bragg gratings

In this paper, we theoretically analyze the slow-light π-phase-shifted fiber Bragg grating (π-FBG) and its applications for single and multipoint/quasi-distributed sensing. Coupled-mode theory (CMT) and transfer matrix method (TMM) are used to establish the numerical modeling of slow-light π-FBG. The impact of slow-light FBG parameters, such as grating length (L), index change (Δn), and loss coefficient (α) on the spectral properties of π-FBG along with strain and thermal sensitivities are presented. Simulation results show that for the optimum grating parameters L = 50 mm, Δn = 1.5×10⁻⁴, and α = 0.10 m^-1, the proposed slow-light π-FBG is characterized with a peak transmissivity of 0.424, the maximum delay of 31.95 ns, strain sensitivity of 8.380 με^-1, and temperature sensitivity of 91.064 °C^-1. The strain and temperature sensitivity of proposed slow-light π-FBG is the highest as compared to the slow-light sensitivity of apodized FBGs reported in the literature. The proposed grating have the overall full-width at half maximum (FWHM) of 0.2245 nm, and the FWHM of the Bragg wavelength peak transmissivity is of 0.0798 pm. The optimized slow-light π-FBG is used for quasi-distributed sensing applications. For the five-stage strain quasi-distributed sensing network, a high strain dynamic range of value 1469 με is obtained for sensors wavelength spacing as small as 2 nm. In the case of temperature of quasi-distributed sensing network, the obtained dynamic range is of 133 °C. For measurement system with a sufficiently wide spectral range, the π-FBGs wavelength grid can be broadened which results in substantial increase of dynamic range of the system.     

An impact excitation system for repeatable,high-bandwidth modal testing of miniature structures

Miniature components and devices are increasingly seen in a myriad of applications. In general, the dynamic behavior of miniature devices is critical to their functionality and performance. However, modal testing of miniature structures poses many challenges. This paper presents a design and evaluation of an impact excitation system (IES) for repeatable, high-bandwidth, controlled-force modal testing of miniature structures. Furthermore, a dynamic model of the system is derived and experimentally validated to enable the identification of the system parameters that yield single-hit impacts with desired bandwidth and force magnitude. The system includes a small instrumented impact tip attached to a custom designed flexure-based body, an automated electromagnetic release mechanism, and various precision positioners. The excitation bandwidth and the impact force magnitude can be controlled by selecting the system parameters. The dynamic model of the system includes the structural dynamics of the flexure-based body, the electromagnetic force and the associated eddy-current damping, and the impact event. A validation study showed an excellent match between the model simulations and experiments in terms of impact force and bandwidth. The model is then used to create process maps that relate the system parameters to the number of hits (single vs. multiple), the impact force magnitudes and the excitation bandwidths. These process maps can be used to select system parameters or predict system response for a given set of parameters. A set of experiments is conducted to compare the performances of the IES and a (manual) miniature impact hammer. It is concluded that the IES significantly improves repeatability in terms of the impact bandwidth, location, and force magnitude, while providing a high excitation-bandwidth and excellent coherence values. The application of the IES is demonstrated through modal testing of a miniature contact-probe system.     

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.     

Numerical simulation of deformation and fracture of a material with a polysilazane-based coating

The paper studies the localization of plastic deformation and fracture in a material with a porous coating. A dynamic boundary value problem in the plane strain formulation is solved. The numerical simulation is performed by the finite difference method. The composite structure corresponds to the experimentally observed one and is specified explicitly in the calculation. A generation procedure of the initial finite-difference grid is developed to describe the coating structure with adjustable porosity and geometry of the substrate-coating interface. Constitutive equations for the steel substrate include an elastic-plastic model of an isotropically hardening material. The ceramic coating is described by a brittle fracture model on the basis of the Huber criterion which accounts for crack nucleation in triaxial tension zones. It is shown that the specific character of deformation and fracture of the studied composite results from the presence of local tensile regions in the vicinity of pores and along the coating-substrate interface, in both tension and compression of the coated material. The interrelation between inhomogeneous plastic flow in the steel substrate and crack propagation in the coating is studied.     

Development of high-temperature Kolsky compression bar techniques for recrystallization investigation

We modified the design originally developed by Kuokkala’s group to develop an automated high-temperature Kolsky compression bar for characterizing high-rate properties of 304L stainless steel at elevated temperatures. Additional features have been implemented to this high-temperature Kolsky compression bar for recrystallization investigation. The new features ensure a single loading on the specimen and precise time and temperature control for quenching to the specimen after dynamic loading. Dynamic compressive stress-strain curves of 304L stainless steel were obtained at 21, 204, 427, 649, and 871 °C (or 70, 400, 800, 1200, and 1600 °F) at the same constant strain rate of 332 s⁻¹. The specimen subjected to specific time and temperature control for quenching after a single dynamic loading was preserved for investigating microstructure recrystallization.     

A new method for the determination of damping in cocured composite laminates with embedded viscoelastic layer

A new method for the determination of damping in cocured composite laminates with embedded viscoelastic layer is developed based on mode superposition and modal strain energy method. The calculated damping value is not modal loss factor but a combination of damping from the contributing modes. The dynamic mechanical properties of the viscoelastic material cocured with composites were investigated and were substituted in the present method for calculating the damping in cocured composites. The analytical results were compared with the experimental results by dynamic mechanical thermal analysis (DMTA). The results demonstrate a good agreement between analytical and experimental results. This work provides a means for the study of damping in this structure with different environment temperature and excited frequency.     

Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter

Good performance with small ensemble filters applied to models with many state variables may require ‘localizing’ the impact of an observation to state variables that are ‘close’ to the observation. As a step in developing nearly generic ensemble filter assimilation systems, a method to estimate ‘localization’ functions is presented. Localization is viewed as a means to ameliorate sampling error when small ensembles are used to sample the statistical relation between an observation and a state variable. The impact of spurious sample correlations between an observation and model state variables is estimated using a ‘hierarchical ensemble filter’, where an ensemble of ensemble filters is used to detect sampling error. Hierarchical filters can adapt to a wide array of ensemble sizes and observational error characteristics with only limited heuristic tuning. Hierarchical filters can allow observations to efficiently impact state variables, even when the notion of ‘distance’ between the observation and the state variables cannot be easily defined. For instance, defining the distance between an observation of radar reflectivity from a particular radar and beam angle taken at 1133 GMT and a model temperature variable at 700 hPa 60 km north of the radar beam at 1200 GMT is challenging. The hierarchical filter estimates sampling error from a ‘group’ of ensembles and computes a factor between 0 and 1 to minimize sampling error. An a priori notion of distance is not required. Results are shown in both a low-order model and a simple atmospheric GCM. For low-order models, the hierarchical filter produces ‘localization’ functions that are very similar to those already described in the literature. When observations are more complex or taken at different times from the state specification (in ensemble smoothers for instance), the localization functions become increasingly distinct from those used previously. In the GCM, this complexity reaches a level that suggests that it would be difficult to define efficient localization functions a priori. There is a cost trade-off between running hierarchical filters or running a traditional filter with larger ensemble size. Hierarchical filters can be run for short training periods to develop localization statistics that can be used in a traditional ensemble filter to produce high quality assimilations at reasonable cost, even when the relation between observations and state variables is not well-known a priori. Additional research is needed to determine if it is ever cost-efficient to run hierarchical filters for large data assimilation problems instead of traditional filters with the corresponding total number of ensemble members.     

The mass normalization of the displacement and strain mode shapes in a strain experimental modal analysis using the mass-change strategy

The classic experimental modal analysis (EMA) is a well-known procedure for determining the modal parameters. The less frequently used strain EMA is based on a response measurement using strain sensors. The results of a strain EMA are the modal parameters, where in addition to the displacement mode shapes the strain mode shapes are also identified. The strain EMA can be used for an experimental investigation of a stress–strain distribution without the need to build a dynamical model. It can also be used to determine the modal parameters when, during modal testing, a motion sensor cannot be used and so a strain sensor is used instead. The displacement and strain mode shapes that are determined with the strain EMA are not mass normalized (scaled with respect to the orthogonality properties of the mass-normalized modal matrix), and therefore some dynamical properties of the system cannot be obtained. The mass normalization can be made with the classic EMA, which requires the use of a motion sensor. In this research a new approach to the mass normalization in the strain EMA, without using a motion sensor, is presented. It is based on the recently introduced mass-change structural modification method, which is used for the mass normalization in an operational modal analysis. This method was modified in such a way that it can be used for the mass normalization in the strain EMA. The mass-normalized displacement and strain mode shapes were obtained using a combination of the proposed approach and the strain EMA. The proposed approach was validated on real structures (beam and plate).     

SHI induced nano track polymer filters and characterization

Swift heavy ion irradiation produces damage in polymers in the form of latent tracks. Latent tracks can be enlarged by etching it in a suitable etchant and thus nuclear track etch membrane can be formed for gas permeation / purification in particular for hydrogen where the molecular size is very small. By applying suitable and controlled etching conditions well defined tracks can be formed for specific applications of the membranes. After etching gas permeation method is used for characterizing the tracks. In the present work polycarbonate (PC) of various thickness were irradiated with energetic ion beam at Inter University Accelerator Centre (IUAC), New Delhi. Nuclear tracks were modified by etching the PC in 6N NaOH at 60 (±1) °C from both sides for different times to produce track etch membranes. At critical etch time the etched pits from both the sides meet a rapid increase in gas permeation was observed. Permeability of hydrogen and carbon dioxide has been measured in samples etched for different times. The latent tracks produced by SHI irradiation in the track etch membranes show enhancement of free volume of the polymer. Nano filters are separation devices for the mixture of gases, different ions in the solution and isotopes and isobars separations. The polymer thin films with controlled porosity finding it self as best choice. However, the permeability and selectivity of these polymer based membrane filters are very important at the nano scale separation. The Swift Heavy Ion (SHI) induced nuclear track etched polymeric films with controlled etching have been attempted and characterized as nano scale filters.      

Finely striped structure at the edges of localized deformation bands

Under conditions of high-rate loading, plastic strain localization is a result of tension in the zone of interference of unloading waves rather than of thermal softening. At stresses close to the dynamic strength of the material, the microstructure of localized strain bands consists of strongly deformed material, with a large number of incipient microdiscontinuities. At stresses below the Hugoniot elastic limit, the microstructure looks as a set of barely visible stripes. The finely striped structure at the edges of the bands of a spall damage arises as a result of the stretching of initially rounded damage centers attached to the matrix material during dynamic deformation.