A Frequency Response Based Structural Damage Localization Method Using Proper Orthogonal Decomposition

Background/Objective: Early detection of damage in structures can prevent loss of lives and extend their service life. This has drawn considerable attention of researchers to applying Structural Health Monitoring (SHM) to detect structural damage. Wavelet Transform (WT) is a tool utilized to identify damage in structures by using structural responses. In this study, a WT damage detection method using Operational Deflection Shape (ODS) difference is presented. Method: A two-dimensional Continuous Wavelet Transform (CWT) is utilized to decompose the difference between the ODS of the intact and damaged structure to detect and locate damage. To demonstrate the ability of this technique, a numerical model of a steel plate is applied. Findings: The results show that the location of damage influences damage detectability when the decomposed signal is noisy. Improvements: This method eliminates the problem of border distortion experienced when conventional ODS is applied. The methodology shows the proposed techniques’ simplicity while the results show accuracy.Keywords: Cantilever Plate, Continuous Wavelet Transform, Damage Detection, Damage Severity Tree, Deflection Shape

In principal, a proper analysis of the dynamic response of a structure can provide general indicators of its operational conditions. When the dynamic response changes due to a variation of the physical properties of a structure, then one may conclude that some kind of damages has occurred. This paper presents investigation of the robustness and comparison of four simple methodologies to both identify and quantify the damages in structures, based on the use of Frequency Response Functions (FRF) signals, Principal Component Analysis technique (PCA) and Transmissibility. A steel beam with constant rectangular cross-section is used to compare the proposed approaches. At first, nine damaged scenarios are created and for each of them numerical examples are discussed; a database of FRFs is measured using modal testing. Then, PCA theory is applied to the FRF matrix and global damage detection and quantification indices are defined by using the first 3 Principal Components; Hotelling's T-squared distribution is also applied and by using transmissibility two other indicators, Transmissibility Damage Indicator and Weighted Damage Indicator, are computed for the assessment of damage. The reported examples show that all proposed methods are able to detect and quantify damages at the initial stage.

Stiffness-based structural health monitoring methods are widely used for detecting the damage in a structure. These stiffness-based structural health monitoring methods uses change in natural frequencies and modeshapes for damage detection. These methods are based on identifying the change in stiffness of the healthy and damage structure to predict the damage in the structure. These stiffness-based methods are not efficient for detecting a small damage in a structure as there is a negligible change in natural frequencies and modeshapes due to a small damage in a structure, however the damping characteristics of the structure are highly sensitive to the damage in a structure. In this paper, new damping-based damage detection procedure has been proposed. In the proposed procedure, the changes in damping matrix of the structure has been used to detect the damage in the structure. The proposed procedure is able (or can) to detect both the location of the damage and the extend of the damage in the structure. The proposed procedure of damping-based damage detection is a 2-step procedure. In the first step, damping matrices of both the healthy and damage structure are identified and in the second step, the identified damping matrices are used for damage detection. Numerical and experimental case studies are presented to demonstrate the effectiveness of the proposed procedure. The results have shown that the proposed damping-based damage detection procedure can be used for detecting damage in a structure with confidence.

Crack location identification, as one key destination of structural health monitoring, is still a challenge for operating rotor systems. The operating deflection shape (ODS), which represents a visual description of the structural vibration patterns under operating conditions, has been gaining importance for structure damage detection in recent years. The ODS carries damage information of a structure, however, it is also difficult to detect weak cracks of rotor directly. The approximate waveform capacity dimension (AWCD) method was successfully applied to damage detection of plates and beam-like structures. In this paper, a strategic approach that combines ODS and weighted AWCD is proposed for crack location identification of the rotating rotor. To eliminate the false peaks of AWCD and obtain desirable results, a weight factor and ODS curvature data are introduced to the expression of the weighted AWCD. The effectiveness of the proposed method is validated by numerical simulation and experimental investigation in a cracked rotor system. The results indicate that the proposed approach not only provides good identifying performance for incipient rotor cracks, but also effectively eliminates the fault peaks introduced by the inflexion locations of ODSs. Moreover, the proposed approach proves promising in detecting crack locations of rotating rotor systems.

High-speed digital image correlation is a camera-based displacement measurement technique that has experienced increasing popularity for modal analysis. It is due to a high spatial density of measurement that provides an outstanding interpretation of mode shapes or operational deflection shapes. However, its sensitivity is typically lower than other techniques and transducers such as accelerometers or laser vibrometry. With these measurements, the estimation of any transfer function in the frequency domain is noisier in valley regions of the response, including anti-resonances. Therefore, an accurate analytical model of the response should be used for modal identification. Modal analysis algorithms perform an identification of the modal parameters and a reconstruction of the response based on the transfer function between force excitation and displacement response. This is called the frequency response function. However, force measurements are not available in many experiments, where the motion excitation is recorded instead. This is the case when the vibration is applied to the specimen through a motion in its base. This transfer function, also known as the transmissibility function, relates the motion of excitation and response, whose shape differs from the frequency response function. This difference in the response function is relevant in a relatively noisy measurement like using digital image correlation. Hence, in this work, a transformation of the transmissibility function into equivalent frequency response function, based on theoretical models, is performed prior to modal identification in base motion tests. More suitable experimental response functions are obtained, increasing the accurateness of the modal parameter estimation.KeywordsModal analysisTransmissibility functionsFull-field measurement

Identification of Weakly Nonlinear Systems Using Describing Function Inversion

Structural damage detection from measured vibration responses has gain popularity among the research community for a long time. Damage is identified in structures as reduction of stiffness and is determined from its sensitivity towards the changes in modal properties such as frequency, mode shape or damping values with respect to the corresponding undamaged state. Damage can also be detected directly from observed changes in frequency response function (FRF) or its derivatives and has become popular in recent time. A damage detection algorithm based on FRF curvature is presented here which can identify both the existence of damage as well as the location of damage very easily. The novelty of the present method is that the curvatures of FRF at frequencies other than natural frequencies are used for detecting damage. This paper tries to identify the most effective zone of frequency ranges to determine the FRF curvature for identifying damages. A numerical example has been presented involving a beam in simply supported boundary condition to prove the concept. The effect of random noise on the damage detection using the present algorithm has been verified.

Damage indices based on structural dynamic characteristics are often used to detect damage in the structures. In this study, a new index for identifying damages in base-isolated structures is proposed using the frequency response function (FRF). Since calculation of the FRF data is time- and memory-consuming for problems of large size, the two-dimensional principal component analysis technique is employed to decrease the data size. The damage indices calculated, representing the health state of the structure, are stored in a database, which are then used to detect the damage location and severity by utilizing the lookup table method. The proposed damage detection method is applied to four concrete frame models, one of which is fixed at the base and the others are isolated by elastomeric bearings. The FRF data are polluted with three different noise values (5%, 10% and 15%) in order to evaluate the uncertainty of measurements. The accuracy of the proposed indices is compared with each other for various parameters such as noise values, bearings characteristics, base conditions and different damage scenarios. The results show the precision of the proposed method.

Structural damages usually introduce nonlinearity to the system. A previously developed nonlinear identification method is employed to detect crack type structural damage. The method requires the measurement of FRFs at various points in order to locate the damage. The method makes it also possible to determine the extent of damage by identifying the level of nonlinearity. The verification of the method is demonstrated with experimental case studies using beams with different levels of cracks. The approach proposed in this study is very promising to be used in practical systems, but still open to further improvements.

Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. The algorithms make use of a finite-element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite-element model. In this work, the concept of the minimum rank perturbation theory (MRPT) is adopted to determine the damage extent on the mass properties of an undamped structure. In addition, the MRPT is extended to the case of proportionall y damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping, or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented. HE advent of the Space Shuttle has prompted considerable attention to the design and control of large space structures. Due to the large size and complexity of envisioned structures, as well as the use of advanced materials to reduce structural weight, it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs. From experience gained in the machinery health monitoring field, one would expect the vibration signature of the structure, either frequency response functions and/or modal parameters, to provide useful information in determining the location and extent of structural damage. Assume that a refined finite element model (FEM) of the structure has been developed before damage has occurred. By refined, we mean that the measured and analytical modal properties are in agreement. Next, assume that at a later date some form of structural damage has occurred. If significant, the damage will result in a change in the structures modal parameters. The question is: can the discrepancy between the original FEM modal properties and postdamage modal properties be used to ascertain structural damage? Most prior work in damage detection has used the general framework of FEM refinement (system identification) in the development of damage assessment algorithms. The motivation behind the development of FEM refinement techniques is based on the need to validate engineering FEMs before their acceptance as the basis for final design analysis. The standard problem has been to seek a refined FEM that is as close to the original FEM and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation. A considerable amount of work in this area has been

Damage detection in an offshore platform using incomplete noisy FRF data by a novel Bayesian model updating method

In the automobile industry, impact force is the main cause for material fatigue in lightweight vehicles. Bump-excited impact force is the most common case, which causes damage to vehicles and reduces the quality of the ride. Force identification is important to reflect the structure's health so that action such as structure modification can be taken before material fatigue. However, direct measurement by using force transducer is not practical due to difficulty in force sensor configuration. A methodology utilizing Operating Deflection Shape (ODS) analysis, Frequency Response Function (FRF) measurement and Modal Transformation Method (MTM) to evaluate the dynamic force is proposed here. This method is called indirect force measurement by using inverse technique. The performance of this approach was demonstrated via experiment. From the measured responses and measured dynamic characteristics of an automobile test rig, a real time mathematical manipulation can generate the systems input force. The force location is known in priori for impact excitation and therefore the inverse problem is well-posed. This method was tested using different force location with unique input force. It shows that high quality of curve fitting to extract the modal parameters such as damped natural frequency, modal damping and residue mode shape is essential to obtain a high accuracy force determination result.

Summary An efficient approach to identify multiple cracks in a slender beam using the frequency response function data is presented. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a slender beam. The cracks are modeled by rotational springs and the frequency response function is computed based on a spectral element model by the spectral finite element. The procedure gives a linear relationship explicitly between the changes of the measured frequency response function and crack parameters. The inverse problem is solved iteratively for the depths and locations of the cracks through the sensitivity-based model updating. Some numerically simulated tests on beam examples are provided for validating the feasibility of the method to identify the cracks. The results are generally agreement with the target values. Finally, the effect of noise on the damage identification is discussed in the numerical examples.

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of rapidly obtaining spatially dense operating deflection shapes (ODSs) by continuously sweeping a laser spot from the system over a structure surface. This paper presents a new damage identification methodology for beams that uses their ODSs under sinusoidal excitation obtained by a CSLDV system, where baseline information of associated undamaged beams is not needed. A curvature damage index (CDI) is proposed to identify damage near a region with high values of the CDI at an excitation frequency. The CDI uses the difference between curvatures of ODSs associated with ODSs that are obtained by two different CSLDV measurement methods, i.e., demodulation and polynomial methods; the former provides rapid and spatially dense ODSs of beams, and the latter provides ODSs that can be considered as those of associated undamaged beams. Phase variables are introduced to the two methods for damage identification purposes. The proposed damage identification methodology was experimentally validated on a beam with damage in the form of machined thickness reduction. The damage and its region were successfully identified in neighborhoods of prominent peaks of CDIs at different excitation frequencies.

The structural characteristic deflection shapes (CDS’s) such as mode shapes and operational deflection shapes are highly sensitive to structural damage in beam- or plate-type structures. Nevertheless, they are vulnerable to measurement noise and could result in unacceptable identification errors. In order to increase the accuracy and noise robustness of damage identification based on CDS’s using vibration responses of random excitation, joint approximate diagonalization (JAD) technique and gapped smoothing method (GSM) are combined to form a sensitive and robust damage index (DI), which can simultaneously detect the existence of damage and localize its position. In addition, it is possible to apply this approach to damage identification of structures under ambient excitation. First, JAD method which is an essential technique of blind source separation is investigated to simultaneously diagonalize a set of power spectral density matrices corresponding to frequencies near a certain natural frequency to estimate a joint unitary diagonalizer. The columns of this joint diagonalizer contain dominant CDS’s. With the identified dominant CDS’s around different natural frequencies, GSM is used to extract damage features and a robust damage identification index is then proposed. Numerical and experimental examples of beams with cracks are used to verify the validity and noise robustness of JAD based CDS estimation and the proposed DI. Furthermore, damage identification using dominant CDS’s estimated by JAD method is demonstrated to be more accurate and noise robust than by the commonly used singular value decomposition method.