A probabilistic damage detection approach using vibration-based nondestructive testing

Automated finite element model updating of a scale bridge model using measured static and modal test data

The quantities of interest in geosciences (e.g., atmospheric wind, rock porosity) typically exhibit structure across a wide range of spatial and temporal scales. As a result, it is insufficient to define measurement errors as some deviations from a reference truth. The main issue is that different instruments and models filter reality in distinct ways. Without a precise mathematical description of this filtering, the exact nature of measurement, model, and representation errors remains unclear. To address this, a measurement model that specifies which geophysical field is being sampled and where is proposed. Based on this model, formal definitions for measurement, model, and representation errors are given. The distinction between these types of errors is also discussed. A novel aspect of this study is the demonstration of conditions under which measurement and representation errors will be correlated with one another. Using this new framework, two common measurement error estimation methods, namely the triple‐cornered hat and triple collocation, are shown to be special cases of a more general approach, called sampling‐aware field‐informed retrieval, that explicitly accounts for representation error. Idealized experiments are conducted to illustrate how this general approach performs in various measurement error estimation scenarios involving representation errors. In the more realistic scenarios where observations originate from differently sized sampling windows and are not perfectly collocated with one another, it is shown that estimating measurement errors is possible only if representation errors are accounted for. It is also demonstrated that displacement errors must be taken into account to avoid correlations between measurement and representation errors. More generally, this study advocates that the formulation of a measurement model is necessary for the measurement and representation errors to be clearly defined.

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

Structural health monitoring (SHM) of bridges and, in particular, the development of efficient and reliable damage detection methodologies have been given a huge attention over the last three decades, by both the scientific community and bridge owners. Damage detection techniques involve the comparison of the structure’s response obtained in the monitoring stage with that of a baseline condition. The damage detection process generally involves five increasing knowledge steps ranging between, in a first stage, signalizing the occurrence of damage and, in a last stage, assessing its effects on the safety and lifecycle of the bridge. Therefore, detailed assessment and characterization of the in-service behaviour of the structure is paramount for successfully completing the damage detection process. With the aim of applying sound damage detection approaches based on the quasi-static component of moving-load responses in concrete bridges, this paper is devoted to the analysis of the in-service behaviour of these structures under moving-loads. A reduced-scale laboratorial model of a reinforced and prestressed concrete frame, subjected to a moving-load, was chosen as the case study. Although the laboratorial structure is not a scaled down model of a bridge, the authors believe that its response is representative of the behaviour of typical full-scale frame concrete bridges. Furthermore, it is noteworthy that smeared cracking might be observed along the frame’s beam, which is typical in concrete bridges. The structure under analysis was subjected to an extensive set of experimental tests, which comprised the observation of the structural response during the passage of a moving point-load, both forward and backwards, for different loads and under different prestress force scenarios (Cavadas & Figueiras 2014). That study revealed that, even though the pre-existing cracks remain entirely under compression (thanks to the applied prestressing forces) during the passage of the moving load, the structure exhibits a non-linear behaviour. This behaviour has important implications in the context of the application of damage detection techniques to cracked beam structures. On the one hand, it implies that the experimental influence lines become dependent on the direction of moving loads. This fact was evident in the experimental tests, where different influence lines for displacements, rotations and strains were obtained for forward and backward movement directions. On the other hand, the non-linear behaviour also implies that the beam’s deformations due to a constant point load will change if the prestressing force is modified. In this context, the main purpose of the present paper consists in the discussion and justification of the nonlinear behaviour observed in the laboratorial model. For that purpose, detailed finite element analyses were conducted. Nonlinear constitutive models were adopted to simulate the cyclic behaviour of cracked reinforced concrete structures. Special attention was devoted to the bond-slip behaviour at the interface between the reinforcing bars and the surrounding concrete, and also to the cyclic relationship between the local crack width and the concrete stress normal to the crack. The nonlinearity of concrete in compression was not considered because the structure is subjected to reduced concrete compressive stresses. The supports deformability was also considered in the analyses. Finally, it could be demonstrated that the observed nonlinear response is due to two main reasons: (i) the hysteretic behaviour of cracked reinforced concrete elements, which occurs even when pre-existing cracks are entirely under compression; (ii) the supports deformability. Even though the results and discussions presented in this paper were obtained for a reduced scale laboratorial model, the phenomena under analysis can be found in real structures and therefore, this subject is relevant in the context of the application of damage detection techniques to real bridge structures.

On choice and effect of weight matrix for response sensitivity-based damage identification with measurement and model errors

Large scale tests with progressive damage on a prestressed concrete highway bridge have been performed to investigate the sensitivity of several damage detection, localization, and quantification methods based on modal parameters. To investigate the quality of modal parameters, the data set of one damage step was analyzed by several output-only identification techniques. Although the bridge was severely cracked, natural frequencies as well as mode shapes display only minor changes. However, the relative changes of mode shapes are larger than those observed for natural frequencies. A novel damage indicator, called mode shape area index, based on changes of mode shapes, has been developed and found as the most sensitive damage detection approach. Damage detection or localization via changes of the flexibility matrix performed better than natural frequencies or mode shapes alone. The application of the direct stiffness calculation and a sensitivity-based model update technique showed results having a high level of ambiguity about the location and quantification of damage also at the highest damage level. Evaluating the information collected in this study the test results indicate that an early stage damage identification in prestressed concrete bridges is hardly possible because of the nearly complete recovery of stiffness after closing of cracks in prestressed concrete and the effect of environmental parameters on modal data.

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three-dimensional frame structure and real vibration data for a three-storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.

Structural damage and its extent can be detected by vibration-based techniques to avoid failure or to minimize maintenance. Among different damage identification techniques, modal curvature approaches are widely researched and applied one. On the contrary, wavelet transformation (WT) methods are gaining popularity in damage identification of real life buildings because of their suitability for non-stationary signals and non-dependency on baseline data. This paper presents a novel approach utilizing complex continuous wavelet to effectively locate change in physical properties of reinforced concrete (RC) buildings by virtue of variation in frequency and mode shapes due to small change in mass and stiffness. In this paper, the effect of variation of mass and stiffness of a building on the modal parameters is established analytically using theequation of motion for a multi-degree freedom system under forced vibration condition. A 3-D finite element model was developed for predicting the modal frequencies and mode shapes of the scaled down six storey RC building and the effect of addition of mass on a particular level of structure on the modal parameters was studied. Further, acceleration time histories were recorded with variation in mass on 3rd story of building using wireless tri-axial accelerometers and the time histories were processed to arrive at Curvature Damage Factor and wavelet coefficients for identification of the additional load on the particular floor. Vibration responses from all floors of RC building in ambient and loaded conditions were analyzed for frequency response spectra (FRS). Mode shapes were drawn for unloaded case and loaded cases. It was observed that the modal frequency of building decreases with the increase in mass at floors. It is observed that CDF approach could detect the change in mass in both numerical and experimental results. However, CDF algorithm could not detect the addition of load in case 1, 2 and 3, i.e. when load was less than 25 kg, i.e. only 2.6% of floor mass (960 kg). The acquired data for the above stated load cases were analyzed using complex Gaussian ‘cgau5’ wavelet in MATLAB toolbox to determine the singularity in the signal in terms of wavelet coefficient modulus. It is observed that the WT approach is able to precisely locate the change in physical parameters of the RC model building. However, it is seen that additional load could not be detected in case where only 9 kg, i.e. 0.93% of the total floor mass, was placed on 3rd floor. From the research work, it is observed that CDF technique is inefficient in damage detection and always demand prior baseline information, which is usually difficult to obtain in practice. However, the wavelet transform-based approach more accurately detects the location of change without relying on intact state vibration data.

We propose a substructure approach that allows for the local damage detection of a shear structure. This method requires only three sensors to identify localized damage in any story of a shear structure building. A substructure approach was used in this method to divide a complete structure into several substructures in order to significantly reduce the number of unknown parameters for each substructure so that damage detection processes can be independently conducted on each substructure. Thus, our method is suitable for use in a parallel and distributed damage detection system. Simulations and experiments on five-story buildings were conducted to test the feasibility of our proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

A damage detection process can be significantly enhanced if the nonlinear effects can be used when extracting damage-sensitive features from measured signals. The coherence function is typically used for nonlinearity identification by determining the extent of the output power linearly correlated with the input. However, the excitations are usually difficult to measure in actual tests. To overcome this limit, this article presents a signal-segments cross-coherence method for nonlinearity identification. By defining a signal-segments cross-coherence matrix and signal-segments cross-coherence index, the method can visually and quantitatively indicate the presence of nonlinearity. The innovation of the new method is that the coherence analysis process only depends on a single output signal, where input and baseline signals are not required. Then, a novel structural damage localization index is constructed by multi-point comparing of the signal-segments cross-coherence indices, based on the assumption that all the measured signals from different points on the structure have the same frequency bandwidth and components. To meet this requirement, a newly proposed signal decomposition method called analytic mode decomposition method is adopted. Numerical studies on a duffing oscillator and a 10 degree-of-freedom spring-damping-mass system were performed to demonstrate the nonlinear identification process and investigate the effectiveness and robustness of the signal-segments cross-coherence-based damage detection method. The results show that the signal-segments cross-coherence method can effectively indicate the appearance of nonlinearity by the signal-segments cross-coherence matrix and signal-segments cross-coherence index with strong noise robustness. And the proposed damage localization index can accurately detect the weak nonlinear damage even with severely noise-polluted signals. To further investigate the applicability of the new method, an experimental study was conducted on a steel simplified scale model of a monopile offshore wind turbine support structure. The results demonstrate that the proposed signal-segments cross-coherence method and the new damage localization index can be used to detect the bolt-loosening damage of the steel structure only with output signals.

To identify the damaged beams in large-scale spatial structure, a damage indicator based on virtual axial strain calculated from mode shape vectors was proposed. The damage detection process was performed based on the dynamic simulation flowchart. Firstly, random signals were used for excitation and the damage was simulated by decreasing beam elasticity modulus. Then, the NEWMARK-β precision direct integral method was appreciated for calculating time history response. Finally, the frequency-domain decomposition method only using output response signal was selected for modal parameter estimation. A double-layer grid structure was taken as example for verifying the damage detection method. Results indicate that the proposed indicator was insensitive to environmental noise and capable of localizing multiple damaged members in space structure without the baseline data.

In this paper, a vibration-based damage detection method designed for thin plates is proposed. The method bases on the relation existing between the strain energy stored in the plate in several vibration modes and the respective natural frequencies. For any mode, the strain energy results as sum of the energies stored in all plate elements in that mode. It depends on the square of the mode shape curvature achieved in each element location for the given vibration mode. As a result, the energy distribution along the plate is different for each mode. By reducing the rigidity of one plate element due to a damage, the frequencies will drop in a different manner, depending on the damaged element location. This permits to define patterns that characterize the dynamic behavior of the plated for any damage location. Actually, the patterns are derived from the normalized frequency shifts attained by numerical simulations. Herein the patterns that characterize a centrally located damage of different extent are consequently derived by means of the finite element analysis and used as a benchmark in the damage detection process. These patterns are successfully used to recognize, localize and quantify damages from measurements on in real plates.

As a new medium for questionnaire delivery, the internet has the potential to revolutionise the survey process. Online (web-based) questionnaires provide several advantages over traditional survey methods in terms of cost, speed, appearance, flexibility, functionality, and usability [1, 2]. For instance, delivery is faster, responses are received more quickly, and data collection can be automated or accelerated [1- 3]. Online-questionnaires can also provide many capabilities not found in traditional paper-based questionnaires: they can include pop-up instructions and error messages; they can incorporate links; and it is possible to encode difficult skip patterns making such patterns virtually invisible to respondents. Like many new technologies, however, online-questionnaires face criticism despite their advantages. Typically, such criticisms focus on the vulnerability of online-questionnaires to the four standard survey error types: namely, coverage, non-response, sampling, and measurement errors. Although, like all survey errors, coverage error (“the result of not allowing all members of the survey population to have an equal or nonzero chance of being sampled for participation in a survey” [2, pg. 9]) also affects traditional survey methods, it is currently exacerbated in online-questionnaires as a result of the digital divide. That said, many developed countries have reported substantial increases in computer and internet access and/or are targeting this as part of their immediate infrastructural development [4, 5]. Indicating that familiarity with information technologies is increasing, these trends suggest that coverage error will rapidly diminish to an acceptable level (for the developed world at least) in the near future, and in so doing, positively reinforce the advantages of online-questionnaire delivery. The second error type – the non-response error – occurs when individuals fail to respond to the invitation to participate in a survey or abandon a questionnaire before it is completed. Given today’s societal trend towards self-administration [2] the former is inevitable, irrespective of delivery mechanism. Conversely, non-response as a consequence of questionnaire abandonment can be relatively easily addressed. Unlike traditional questionnaires, the delivery mechanism for online-questionnaires makes estimation of questionnaire length and time required for completion difficult1, thus increasing the likelihood of abandonment. By incorporating a range of features into the design of an online questionnaire, it is possible to facilitate such estimation – and indeed, to provide respondents with context sensitive assistance during the response process – and thereby reduce abandonment while eliciting feelings of accomplishment [6]. For online-questionnaires, sampling error (“the result of attempting to survey only some, and not all, of the units in the survey population” [2, pg. 9]) can arise when all but a small portion of the anticipated respondent set is alienated (and so fails to respond) as a result of, for example, disregard for varying connection speeds, bandwidth limitations, browser configurations, monitors, hardware, and user requirements during the questionnaire design process. Similarly, measurement errors (“the result of poor question wording or questions being presented in such a way that inaccurate or uninterpretable answers are obtained” [2, pg. 11]) will lead to respondents becoming confused and frustrated. Sampling, measurement, and non-response errors are likely to occur when an online-questionnaire is poorly designed. Individuals will answer questions incorrectly, abandon questionnaires, and may ultimately refuse to participate in future surveys; thus, the benefit of online questionnaire delivery will not be fully realized. To prevent errors of this kind2, and their consequences, it is extremely important that practical, comprehensive guidelines exist for the design of online questionnaires. Many design guidelines exist for paper-based questionnaire design (e.g. [7-14]); the same is not true for the design of online questionnaires [2, 15, 16]. The research presented in this paper is a first attempt to address this discrepancy. Section 2 describes the derivation of a comprehensive set of guidelines for the design of online-questionnaires and briefly (given space restrictions) outlines the essence of the guidelines themselves. Although online-questionnaires reduce traditional delivery costs (e.g. paper, mail out, and data entry), set up costs can be high given the need to either adopt and acquire training in questionnaire development software or secure the services of a web developer. Neither approach, however, guarantees a good questionnaire (often because the person designing the questionnaire lacks relevant knowledge in questionnaire design). Drawing on existing software evaluation techniques [17, 18], we assessed the extent to which current questionnaire development applications support our guidelines; Section 3 describes the framework used for the evaluation, and Section 4 discusses our findings. Finally, Section 5 concludes with a discussion of further work.

Recognition that measurement error in the independent (predictor) variable of data used for regression modeling necessitates special methods of model fitting dates back to the late 1800s. In the ensuing 100 years attention was devoted almost entirely to measurement error in linear regression models, at which time advances in computing opened the door to the nonlinear statistical modeling generally, and to the study of measurement error in nonlinear regression modeling in particular. This article contains an introduction to the problem of measurement error in regression using linear regression measurement error models to illustrate key ideas. It includes a discussion of the types of measurement error commonly studied (classical and Berkson, differential and nondifferential) and how those types arise in practice. A summary of the consequences of ignoring measurement error when analyzing data measured with error is presented, with detailed results given for simple and multiple linear measurement error models. Pointers to the literature on both linear and nonlinear measurement error models are provided.

As carbon fiber reinforced polymer composites (CFRPs) are multifunctional materials in which the damage is coupled with the change in material electrical resistance, the use of electrical conductivity monitoring can provide real-time information concerning the damage state through examining the change in resistance/electric potential. It has been shown that, in some recent work, resistance measurement allows the monitoring of the in-situ evolution of various internal damage nucleation and growth phenomena such as fiber fractures, interply matrix cracks and interply delamination. However, one of the common difficulties in measuring the small changes of electrical signals due to failures in the CFRPs is the contamination of extraneous noises during the detection process. In this paper, signal analysis procedures are applied to minimize or eliminate the contaminated noise during the damage detection process, as to maximize the accuracy of the damage detection process. In addition to the traditional time signal averaging technique, the Fast Fourier Transform (FFT) is applied to filter at the narrow band near the input frequency as to eliminate the unwanted noises. However, based on laboratory experiments, the authors have found that the frequency filtering techniques will retain significant inaccuracy when extraneous noises are in the neighborhood of the input frequency, and, in some cases, accurate measurement of the electrical signals can be susceptable when noise components are significantly higher than the original input signal. To overcome this drawback, the use of a joint time-frequency technique with wavelet transforms has been introduced. As a joint time-frequency signal analysis tool, the wavelet transforms offer simultaneous interpretation of the signal in both time and frequency domains which results in signal filtering effects in both time and frequency domains. Experimental results by the authors have shown significant improvement in accuracy when using the wavelets than those of the FFT and the time averaging techniques. This paper demonstrates the wavelet transform applications in electrical signal noise reduction of CFRPs as well as the use of both continuous wavelet (CWT) and discrete wavelet (DWT) transforms. It has been found that when noise is small, the DWT is more appropriate as the original signal can be reconstructed to offer better comparative information. The use of CWT will provide better results when random noises are significantly higher. Although the use of CWT does not have the ability revert back to the original signal, the comparison of the CWT coefficients can offer more valuable information concerning the damage occurrences while the repeated applications of DWT will result in accumulated errors such that the original shapes of the wavelet cannot be correctly reconstructed.