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Direct model updating schemes modify the entries of system matrices to better match modal data. Thus far this has been done under the constraint imposed by symmetry and, in some cases, zeros from connectivity. Relations between coefficients of the stiffness matrix imposed by equilibrium, however, which are here designated as static constraints, have not been considered. The addition of static constraints to those from symmetry and connectivity completes the set of constraints and restricts the solution space of any direct update to that which is parametrically realizable from the model; eliminating, in this way, the long standing drawback of matrix modifications that have no physical interpretation. Static constraints lead to reductions in the amount of modal data needed to attain a unique solution and, as one anticipates, improve the accuracy of the update, in general. Direct model updating schemes modify the entries of system matrices to better match modal data. Thus far this has been done under the constraint imposed by symmetry and, in some cases, zeros from connectivity. Relations between coefficients of the stiffness matrix imposed by equilibrium, however, which are here designated as static constraints, have not been considered. The addition of static constraints to those from symmetry and connectivity completes the set of constraints and restricts the solution space of any direct update to that which is parametrically realizable from the model; eliminating, in this way, the long standing drawback of matrix modifications that have no physical interpretation. Static constraints lead to reductions in the amount of modal data needed to attain a unique solution and, as one anticipates, improve the accuracy of the update, in general.

This paper introduces a damage detection scheme based on changes in the period of limit cycles (LCs) realized by nonlinear output feedback. The parameterized feedback law is selected to make the dynamic equilibrium of the actuated coordinate approximate that of a generalized van der Pol oscillator and potential model-related difficulties are avoided by fixing the parameters from experimental results. It is found that not all sensor/actuator arrangements are suitable for generating a LC in closed loop, so a methodology to determine which arrangements are viable is presented. Numerical results show that LC periods are adequately stable with respect to noise and system changes from environmental effects and have sensitivity to localized damage that is often orders of magnitude larger than those of the modal frequencies. This paper introduces a damage detection scheme based on changes in the period of limit cycles (LCs) realized by nonlinear output feedback. The parameterized feedback law is selected to make the dynamic equilibrium of the actuated coordinate approximate that of a generalized van der Pol oscillator and potential model-related difficulties are avoided by fixing the parameters from experimental results. It is found that not all sensor/actuator arrangements are suitable for generating a LC in closed loop, so a methodology to determine which arrangements are viable is presented. Numerical results show that LC periods are adequately stable with respect to noise and system changes from environmental effects and have sensitivity to localized damage that is often orders of magnitude larger than those of the modal frequencies.

This paper presents a case study demonstrating how to quantify thevalue of structural health monitoring (SHM), when used optimally inmaintenance planning for wind turbine blades. Maintenance costoptimization is performed using a risk-based approach based onBayesian decision analysis, in which probabilistic models are developedfor blade deterioration processes, blade inspections and SHM systems.The probabilistic SHM system model is based on data from an SHMcampaign with a 225 kW Vestas V27 wind turbine, where an artificialtrailing edge crack of increasing size was introduced. The statisticsderived from this model are applied to the case study concerningmaintenance of an 8 MW offshore wind turbine. It is found that thebenefit of the SHM highly depends on the reliability of the SHM systemand on how SHM observations are used when making decisions oninspections and maintenance. A sensitivity study confirms the generalityof the findings. The paper presents a case study demonstrating the methods used to estimate the value of the information (VoI) delivered by a structural health monitoring (SHM) system. The monitored object is a blade of an operating wind turbine. The case study shows how the maintenance cost optimization can be performed using a risk-based approach cast in a Bayesian decision analysis framework, in which probabilistic models are developed for blade deterioration processes, blade inspections, and SHM systems. The paper also provides a parameter study, which demonstrates how the potential benet of SHM highly depends on the reliability of the utilized SHM system and how the SHM observations are used for decision making on the inspections and maintenance.

This paper presents a probabilistic framework for updating the structural reliability of offshore wind turbine substructures based on digital twin information. In particular, the information obtained from digital twins is used to quantify and update the uncertainties associated with the structural dynamics and load modeling parameters in fatigue damage accumulation. The updated uncertainties are included in a probabilistic model for fatigue damage accumulation used to update the structural reliability. The updated reliability can be used as input to optimize decision models for operation and maintenance of existing structures and design of new structures. The framework is exemplified based on two numerical case studies with a representative offshore wind turbine and information acquired from previously established digital twins. In this context, the effect of updating soil stiffness and wave loading, which constitute two highly uncertain and sensitive parameters, is investigated. It is found that updating the soil stiffness significantly affects the reliability of the joints close to the mudline, while updating the wave loading significantly affects the reliability of the joints localized in the splash zone. The increased uncertainty related to virtual sensing, which is employed to update wave loading, reduces structural reliability. This paper presents a probabilistic framework for updating the structural reliability of offshore wind turbine substructures based on digital twin information. In particular, the information obtained from digital twins is used to quantify and update the uncertainties associated with the structural dynamics and load modeling parameters in fatigue damage accumulation. The updated uncertainties are included in a probabilistic model for fatigue damage accumulation used to update the structural reliability. The updated reliability can be used as input to optimize decision models for operation and maintenance of existing structures and design of new structures. The framework is exemplified based on two numerical case studies with a representative offshore wind turbine and information acquired from previously established digital twins. In this context, the effect of updating soil stiffness and wave loading, which constitute two highly uncertain and sensitive parameters, is investigated. It is found that updating the soil stiffness significantly affects the reliability of the joints close to the mudline, while updating the wave loading significantly affects the reliability of the joints localized in the splash zone. The increased uncertainty related to virtual sensing, which is employed to update wave loading, reduces structural reliability.

An intricacy in vibration-based structural damage detection (VSDD) relates to environmental variabilities (EVs) imposing limitations to the damage detectability. One method that has been put forth to resolve the issue is cointegration. Here, non-stationary vibration features are linearly combined into stationary residuals, which are then employed as damage indices under the assumption that the non-stationarity is governed by environmental variabilities. In the present paper, the feasibility of using cointegration to mitigate environmental variabilities while retaining sensitivity to damage is examined through an experimental study with a steel beam. A temperature-based environmental variability is introduced to the beam by use of a heating cable, while damage is emulated by adding local mass perturbations. The vibration response of the beam in different environmental and structural states is captured and utilized as features in a cointegration-based damage detection scheme. The performance of the scheme is assessed and compared to that of a scheme not accounting for the variability on the basis of the false positive ratio (FPR), the true positive ratio (TPR), and the area under the receiver operating characteristic curve (AUC). The results show that cointegration effectively mitigates the temperature variability and allows for an improved damage detectability compared to that of the scheme without a mitigation strategy.

Structural monitoring of wind turbines often involves the use of a numerical model, which must be regularly updated to yield an adequate representation of the governing dynamics. The model updating can be cast as an inverse problem, in which selected model parameters are estimated by minimizing the discrepancy between experimental target poles and model-predicted ones. An issue that may prevail in this setting is that the problem will be ill-posed, because the number of model parameters to be updated exceeds the number of target poles. The noted issue can be remedied by a virtual implementation of output feedback, which allows for computation of multiple closed-loop (CL) eigenstructures through non-linear transformations of the open-loop transfer matrix. The present paper offers an application study, in which virtual output feedback is used for updating numerical wind turbine models based on CL system poles. In particular, we explore the feasibility of employing the excitation stemming from the blade pitch control system as the input in the open-loop input-output realization required in the virtual output feedback. The methodological concept is outlined, and subsequently the applicability of the procedure is tested numerically in the context of simulations with a finite element model of a parked wind turbine. The preliminary findings suggest that procedures for customizing the pitch excitation to yield sufficient system excitation are required for the CL model updating to be feasible.

The present paper investigates the feasibility of modal expansion-based virtual sensing in the context of offshore wind jacket substructures. For this specific application, issues have been reported when expanding wind-driven brace vibrations and wave-driven vibrations in the splash-zone based on a sensor network placed solely above the sea level. These limitations are addressed in this paper by extending the sensor network with sub-sea vibration sensors and a wave radar sensor, which allow for capturing local brace vibration modes and the wave-driven vibration response. The brace expansion is thus improved by including the local brace vibration modes in the expansion basis, while the representation of wave-driven vibrations is improved by including load-dependent Ritz vectors computed based on input from the wave radar sensor. The merit of the proposed extension is explored using a numerical model of an offshore wind turbine supported by a jacket substructure in a simulation setting with different operational and environmental conditions. It is documented that the extended setup provides an improvement in the expansion-based estimation of both wind- and wave-driven vibrations. The former improvement is particularly relevant for operational cases, while the latter is relevant for idling cases. Despite the documented improvements, a systematic reduction in the expansion quality is observed for higher wind speeds in operational cases for both the basic and the extended setup. It is contended that this phenomenon is due to the operational variability of the controller, which violates the fundamental assumption of the structural system being linear and time-invariant.

Within civil engineering, the inclusion of control strategies is confined to limited application areas due to the practical overhead and an alleged conservatism. This paper presents a simple yet flexible framework for experimental testing of closed-loop structural systems. Compared to alternative existing solutions, the proposed framework requires limited programming knowledge, which heavily simplifies the implementation for the operator and thus reduces the associated practical overhead. The feasibility of the framework is demonstrated through two experimental case studies in which control strategies are used to, respectively, design and implement a hybrid tuned mass damper (TMD) and conduct closed-loop model updating. The case studies exemplify the diversity of control applications within civil engineering, and it is noted that while hybrid TMDs are used in the civil engineering industry, limited experimental application studies exist on closed-loop model updating of structural systems. It is concluded that the presented framework can be applied to cover a variety of structural control applications within civil engineering and the successful implementation of the framework in the two case studies highlights the benefits of feedback control within these applications.

An intricacy in vibration-based structural damage detection (VSDD) relates to environmental variabilities imposing limitations to the damage detectability. One method that has been put forth to resolve the issue is cointegration. Here, non-stationary vibration features are linearly combined into stationary residuals, which are then employed as damage indices under the assumption that the non-stationarity is governed by environmental variabilities. In the present paper, the feasibility of using cointegration to mitigate environmental variabilities while retaining sensitivity to damage is examined through an experimental study with a steel beam. A temperature-based environmental variability is introduced to the beam by use of a heating cable, while damage is emulated by adding local mass perturbations. The vibration response of the beam in different environmental and structural states is captured and utilized as features in a cointegration-based damage detection scheme. The performance of the scheme is assessed and compared to that of a scheme not accounting for the variability on the basis of the false positive ratio (FPR), the true positive ratio (TPR), and the area under the receiver operating characteristic curve (AUC). The results show that cointegration effectively mitigates the temperature variability and allows for an improved damage detectability compared to that of the scheme without a mitigation strategy

The present paper provides a model updating application study concerning the jacket substructure of an offshore wind turbine. The updating is resolved in a sensitivity-based parameter estimation setting, where a cost function expressing the discrepancy between experimentally obtained modal parameters and model-predicted ones is minimized. The modal parameters of the physical system are estimated through stochastic subspace identification (SSI) applied to vibration data captured for idling and operational states of the turbine. From a theoretical outset, the identification approach relies on the system being linear and time-invariant (LTI) and the input white noise random processes; criteria which are violated in this application due to sources such as operational variability, the turbine controller, and non-linear damping. Consequently, particular attention is given to assess the feasibility of extracting modal parameters through SSI under the prevailing conditions and subsequently using these parameters for model updating. On this basis, it is deemed necessary to disregard the operational turbine states---which severely promote non-linear and time-variant structural behaviour and, as such, imprecise parameter estimation results---and conduct the model updating based on modal parameters extracted solely from the idling state. The uncertainties associated with the modal parameter estimates and the model parameters to be updated are outlined and included in the updating procedure using weighting matrices in the sensitivity-based formulation. By conducting the model updating based on in-situ data harvested from the jacket substructure during idling conditions, the maximum eigenfrequency deviation between the experimental estimates and the model-predicted ones is reduced from 30 % to 1 %.

A conventional procedure for structural model updating is to solve an inverse problem with the aim of minimizing the discrepancy between an experimental target feature vector and a model-predicted one. The inverse problem to be solved is often ill-posed as the number of model parameters to be updated typically exceeds the number of target features. One way to confront this issue is to expand the target feature vector through closed-loop model updating, where gains are used to form multiple closed-loop eigenstructures from which target features are obtained. Besides confronting the ill-posedness of the inverse problem, the closed-loop model updating procedure also allows one to tailor the sensitivities of the target features by adequate design of the feedback gains. The present paper offers a comparative study in which the merit of different gain design criteria is examined for closed-loop sensitivity-based model updating. More specifically, the gains will be designed through eigenstructure assignment in an optimization setting where different cost functions, including the nuclear norm and the condition number of the sensitivity matrix, will be tested. Updating results will be shown for a numerical model of a shear building. A conventional procedure for structural model updating is to solve an inverse problem with the aim of minimizing the discrepancy between an experimental target feature vector and a model-predicted one. The inverse problem to be solved is often ill-posed as the number of model parameters to be updated typically exceeds the number of target features. One way to confront this issue is to expand the target feature vector through closed-loop model updating, where gains are used to form multiple closed-loop eigenstructures from which target features are obtained. Besides confronting the ill-posedness of the inverse problem, the closed-loop model updating procedure also allows one to tailor the sensitivities of the target features by adequate design of the feedback gains. The present paper offers a comparative study in which the merit of different gain design criteria is examined for closed-loop sensitivity-based model updating. More specifically, the gains will be designed through eigenstructure assignment in an optimization setting where different cost functions, including the nuclear norm and the condition number of the sensitivity matrix, will be tested. Updating results will be shown for a numerical model of a shear building.

A recently proposed virtual implementation of output feed-back based on signal processing eliminates the practical overhead associated with physical operation in closed loop. Additionally, the virtual implementation facilitates realization of multiple closed-loop systems from a single test in open loop, allows for complex gains, and removes the constraint of closed-loop stability. Care must, however, be exercised in the design of the closed-loop systems, as the errors in these are governed by the intrinsic approximations in the open-loop identification. The present paper offers an examination of this item when the closed-loop systems are designed for parameter estimation in updating of numerical models of structural systems. The differences between physical realization and the proposed virtual implementation are discussed, and the pivotal points outlined are demonstrated in the context of a numerical examination with a structural system.

The set of equations to be solved for parameter estimation in model updating has no unique solution when, as will often be the case in structural applications, the dimensionality of the model exceeds the number of target parameters estimated from experiments. One approach for enlarging the target space is to create closed-loop systems that, in addition, can be designed with pole sensitivities favorable for updating the model. The present paper will focus on designing gains for model updating using a recently proposed virtual implementation of output feedback, which allows computation of several closed-loop systems from a single open-loop realization and removes the constraint of closed-loop stability. The gains are designed through an eigenstructure assignment procedure, in which the model parameters of interest in the updating are divided into two different classes; one where the pole sensitivities with respect to the parameters are to be enhanced and one where they are to be reduced. A numerical example with a structural system is presented that demonstrates the merit of the proposed gain design procedure.

Environmental and operational variabilities (EOVs) are known to pose an issue in structural health monitoring (SHM) systems, as these variabilities can mask the effect of structural damage. Numerous approaches to remove, or, at least, mitigate, the effect of EOVs in SHM applications have been proposed and tested through numerical simulations and in experimental studies. One of the approaches that has exhibited promising potential is cointegration, which, in this particular SHM context, is a technique for singling out and removing common signal trends stemming from the EOVs. In the present paper, the cointegration technique is employed to mitigate the effect of certain EOVs in an experimental, vibration-based damage detection analysis of a wind turbine blade under operating conditions. In the experimental campaign, the installed SHM system was recording blade accelerations and different environmental and operational conditions over a 3.5-month period. In the period, one of the blades was treated in its reference state and in damaged states with a trailing edge opening of increasing size. Based on the available data from these different structural states, it is demonstrated how cointegration can be used to successfully detect the introduced damages under conditions not allowing for direct discrimination between damage and EOVs.

Input shaping is an active control procedure by which vibrations in a structural subdomain are suppressed. Recently, a scheme based on shaped inputs has been proposed for damage localization purposes; cast on the premise that the vibration signature of a structural domain in a damaged phase will be identical to the signature of the healthy, reference counterpart if, for the same loading conditions, the subdomain containing damage is inactive in terms of vibrations. The idea is, thus, to apply controllable inputs that are shaped such that particular vibration quantities (depending on the type of damage one seeks to localize) are suppressed in one subdomain at the time, hereby resulting in damage being localized when the vibration signature induced by the shaped inputs in the damaged phase corresponds to that obtained in the reference phase. The present paper treats an application study that illustrates the damage localization scheme in simulations on a finite element model of an offshore jacket structure exposed to stochastic plane wave fields generated from a directional wave spectrum, and with fluid-structure interaction considered in terms of the Morison equation. In both structural phases, that is, the reference and the damaged one with a single mass perturbation, four inputs to be shaped are applied, and the resulting displacements are extracted from a single spatial location within the model. It is contended that the damage is localized when suppressing displacements (and their time-derivatives) near or, ideally, directly at its location.

This paper presents a recently developed simulation tool, SOFIA (Simulation Of Floaters In Action), suitable for modeling slender bottom founded and moored/freely floating space frame structures exposed to environmental loads. In contrast to traditional rigid body formulations of floating structures, the finite element method is utilized in the implemented numerical approach, which allows for direct output of local section forces and displacements for joint analysis and fatigue calculations. The numerical approach builds upon a partitioned solution procedure, constituted by individual fluid and structure domains, which are coupled through the structural equation of motion. The structural domain is handled by means of the finite element method, while large displacements and stress stiffening effects, exhibited by moored floating structures, are inherently included due to a co-rotational element formulation. The fluid domain is modeled by an appropriate water wave theory, and the hydrodynamic loads are evaluated at the instantaneous fluid-structure interface by means of a relative Morison equation. The equation of motion is solved in time domain, which makes SOFIA capable of handling bottom founded and floating space frame structures that may experience non-linear behavior. To demonstrate the applicability of the simulation tool, numerical examples of a bottom founded and a floating space frame structure are presented.

Today, structural integrity inspections of wind turbine blades are typically carried out by the use of rope or platform access. Since these inspection approaches are both tedious and extremely costly, a need for a method facilitating reliable, remote monitoring of the blades has been identified. In this article, it is examined whether a vibration-based damage localization approach proposed by the authors can provide such reliable monitoring of the location of a structural damage in a wind turbine blade. The blade, which is analyzed in idle condition, is subjected to unmeasured hits from a mounted actuator, yielding vibrations that are measured with a total of 12 accelerometers; of which 11 are used for damage localization. The employed damage localization method is an extended version of the stochastic dynamic damage location vector method, which, in its origin, is a model-based method that interrogates damage-induced changes in a surrogate of the transfer matrix. The surrogate’s quasi-null vector associated with the lowest singular value is converted into a pseudo-load vector and applied to a numerical model of the healthy structure in question, hereby, theoretically, yielding characteristic stress resultants approaching zero in the damaged elements. The proposed extension is based on outlier analysis of the characteristic stress resultants to discriminate between damaged elements and healthy ones; a procedure that previously, in the context of experiments with a small-scale blade, has proved to mitigate noise-induced anomalies and systematic, non-damage-associated adverse effects.

This study demonstrates an application of a previously proposed modal and wavelet analysis-based damage identification method to a wind turbine blade. A trailing edge debonding was introduced to an SSP 34-m blade mounted on a test rig. Operational modal analysis was conducted to obtain mode shapes for undamaged and damaged states of the blade. Subsequently, the mode shapes were analyzed with one-dimensional continuous wavelet transformations for damage identification. The basic idea of the method is that structural damage will introduce local mode shape irregularities which are captured in the continuous wavelet transformation by significantly magnified transform coefficients, thus providing combined damage detection, localization, and size assessment. It was found that due to the nature of the proposed method, the value of the identification results highly depends on the number of employed measurement points. Since a limited number of measurement points were utilized in the experiments, only certain damage-sensitive modes, in which pronounced damage-induced mode shape changes occur, are applicable for valid identification of the damage.

If a subdomain of a structural system is introduced to a perturbation, the resulting shifts in any field quantity outside the boundary of some closed region encompassing the perturbation can be generated from stress fields acting on the aforementioned boundary. In the present paper, this is exploited in the context of structural damage localization to cast the Subspace Exclusion Zone (SEZ) scheme, which locates damage by inspecting the feasibility of generating the observed shifts from actions acting at the boundary of the postulated zones in a model of the structure in question. As such, the SEZ scheme is a forward interrogation that allows for a user-defined localization resolution and, under certain input conditions, operates without the use of system identification. The approach is most conveniently implemented in the Laplace domain and holds at s-values for which the load vector in the reference and the damaged states are proportional. The constraint that ensures exact results in an idealized model context is that the number of measurements outside any considered exclusion zone (EZ) exceeds the number of DOF on its boundary. It is shown, however, that useful results can be obtained with notably smaller sensor counts. The paper illustrates application of the SEZ scheme in simulations and in an experimental setting using a beam subjected to harmonic input.

In this paper a novel Data-Driven Design and Operation approach is introduced for an offshore wind energy application to account for site-specific conditions. Data from operational state of a turbine, e.g. accelerations, strain gauges, and SCADA, are intended to be used in the True Digital Twin concept to improve initial design assumptions. A calibrated numerical model combined with measured loading and response models allows to update the structural reliability and thus quantify the potential inherent conservatism. Given this additional knowledge the lifetime extension of existing structures can be assessed while for future structures their design procedures can be optimized according to a chosen cost function. The conceptual framework for including new information from measurements based on the Bayesian updating is presented in the paper. It is demonstrated how the initially assumed generic uncertainties regarding numerical models and environmental conditions can be consistently updated based on the site-specific data and hence lead to a more reliable design and operation of a structure. New information derived from data is accounted for based on the pre-posterior decision procedures supplemented with robust decision rules.

The problem of closed-loop enhanced sensitivity design is as follows: given a linear, time-invariant system, find a (realizable) feedback gain such that (1) the closed-loop is stable in the reference and the potentially damaged states, and (2) the eigenstructure includes a subset of poles, with desirable derivatives, that lie in a part of the plane where identification is feasible. For state feedback the eigenstructure is typically assignable and stability in the reference state is easily enforced. For output feedback, however, only partial assignment is possible, and it is here shown that the standard SVD design scheme leads to generically unstable eigenstructures when measurands are homogeneous (that is, when all sensors measure displacements, velocities, or accelerations). The mechanics that govern this behavior are clarified and a mitigating strategy that retains the convenience of homogeneous sensing is offered.

Given a structure in a state with any type of perturbation, the steady-state vibrational response will be identical to that in the unperturbed state if the perturbation is rendered dormant and, of course, if the load distribution is the same in the two states. Guided by this principle, a damage localization method is cast that operates on the premise of shaping inputs—whose spatial distribution is fixed—by use of a model, such that these inputs, in one structural subdomain at a time, suppress certain steady-state vibration quantities (depending on the type of damage one seeks to interrogate for). Accordingly, damage is localized when the vibration signature induced by the shaped inputs in the damaged state corresponds to that in the reference state, hereby implying that the approach does not point directly to damage. Instead, it operates with interrogation based on postulated damage patterns, resulting in a system identification-free procedure whose primary merits, besides avoiding the typical bottleneck of system identification, include a low demand on output sensors, robustness towards noise, and conceptual simplicity. The price paid for these merits is reliance on a relatively accurate model of the structure in its reference state and the need for multiple controllable inputs.

A lot of effort is dedicated to monitoring the flow properties in offshore pipelines through measurements at the riser section above sea level, where equipment installation and maintenance are cheaper and easier. However, the multi-phase flow in the pipelines is hard to monitor due to the rapid fluctuation in gas volume fraction (GVF) and varying water cut. This paper presents a new, simple approach that offers flow monitoring through the frequency content in vibration measurements captured by installed accelerometers. Particularly, the methodological premise is to extract flow-induced vibrations from the total vibration response, which, besides the flow, is induced by external excitation from wind, waves and current. The distinguishment between the vibration sources is conducted by use of continues wavelet transformation (CWT), which provides information about the frequency shifts and at what time in-stances they occur. When monitoring the multi-phase flow, the structural information gained from the CWT is then coupled to the flow properties through well-established analytical laws and numerical models

Detecting damages from a global perspective, although still a topic of active research, has been resolved with reasonable success by adapting approaches from the fields of statistical pattern recognition and machine learning. As a result, substantial attention is now addressed to bridging the gap between research and industrial use, and numerous successful application studies have been reported for different types of engineering structures. The present paper follows along this path and contributes with an experimental study concerning damage detection in a reinforced concrete slab based on conventional outlier analysis of captured vibration response. The concrete slab is investigated in five measurement setups; one reference, with an initial dent, and four damaged states in which the dent is extended by blank shots fired into the surface. In each state, the structure is subjected to controlled impulse excitation from an installed electro-mechanical actuator, and the response is captured by 14 accelerometers distributed evenly over the concrete slab. The unique entries in the covariance matrix of these accelerations are employed as the feature in the outlier analysis, where the damage index is the Mahalanobis metric. From a strict academic point of view, the task of globally detecting structural damage, albeit still a topic of active research, has been resolved with reasonable success by adapting approaches from the fields of statistical pattern recognition and machine learning. As a result, substantial attention is now addressed to bridging the gap between research and industrial use, and numerous successful application studies have been reported for different types of engineering structures. The present paper follows along this path and contributes with an experimental study concerning damage detection in a reinforced concrete slab based on conventional outlier analysis of captured vibration response. The concrete slab is investigated in five measurement setups, one reference, with an initial dent, and four damaged states by extending the dent with blank shots fired into the surface. In each state, the structure is subjected to controlled impulse excitation from an installed electro-mechanical actuator. The impulse response is captured by 14 accelerometers distributed evenly over the concrete slab. The entries in the covariance matrix of these accelerations are employed as the feature in the outlier analysis, where the damage index is the Mahalanobis metric.

Facilitating detection of early-stage damage is crucial for in-time repairs and cost-optimized maintenance plans of civil engineering structures. Preferably, the damage detection is performed by use of output vibration data, hereby avoiding modal identification of the structure. Most of the work within the vibration-based damage detection research field assumes that the unmeasured excitation signal is time-invariant with a constant covariance, which is hardly achieved in practice. In this paper, we present a comparison of a new Mahalanobis distance-based damage detection method with the well-known subspace-based damage detection algorithm robust to changes in the excitation covariance. Both methods are implemented in the modal analysis and structural health monitoring software ARTeMIS, in which the joint features of the methods are concluded in a control chart in an attempt to enhance the damage detection resolution. The performances of the methods and their fusion are evaluated in the context of ambient vibration signals obtained from, respectively, numerical simulations on a simple chain-like system and a full-scale experimental example, namely, the Dogna Bridge. The results reveal that the performances of the two damage detection methods are quite similar, hereby evidencing the justification of the new Mahalanobis distance-based approach as it is less computational complex. The control chart presents a comprehensive overview of the progressively damaged structure.

International audience; Damage detection consists of monitoring the deviations of a current system from its reference state, characterized by some nominal property repeatable for every healthy state. Preferably, the damage detection is performed directly on vibration data, hereby avoiding modal identification of the structure. The practical aspect of using only the output measurements cause difficulties because of variations in ambient excitation due to variability in the environmental conditions, like sea, wind, and temperature. In this paper, a new Mahalanobis distance-based damage detection method is studied and compared to the well-known subspace-based damage detection algorithm in the context of two large case studies. Both methods are implemented in the modal analysis and structural health monitoring software ARTeMIS, in which the joint features of the methods are concluded in a control chart in an attempt to enhance the resolution of the damage detection. The damage indicators from both methods are evaluated based on the ambient vibration signals from numerical simulations on a novel offshore support structure and experimental example of a full scale bridge. The results reveal that the performance of the two damage detection methods is similar, hereby implying merit of the new Mahalanobis distance-based approach, as it is less computational complex. The fusion of the damage indicators in the control chart provides the most accurate view on the progressively damaged systems.

Contrary to global modal parameters such as eigenfrequencies, mode shapes inherently provide structural information on a local level. Therefore, this particular modal parameter and its derivatives are utilized extensively for damage identification. Typically, more or less advanced mathematical methods are employed to identify damage-induced discontinuities in the spatial mode shape signals, hereby, potentially, facilitating damage detection and/or localization. However, by being based on distinguishing damage-induced discontinuities from other signal irregularities, an intrinsic deficiency in these methods is the high sensitivity towards measurement noise. In the present paper, a damage localization method which, compared to the conventional mode shape-based methods, has greatly enhanced robustness towards measurement noise is proposed. The method is based on signal processing of a spatial mode shape by means of continuous wavelet transformation (CWT) and subsequent application of a generalized discrete Teager–Kaiser energy operator (GDTKEO) to identify damage-induced mode shape discontinuities. In order to evaluate whether the identified discontinuities are in fact damage-induced, outlier analysis is conducted by applying the Mahalanobis metric to major principal scores of the sensor-located bands of the signal-processed mode shape. The method is tested analytically and benchmarked with other mode shape-based damage localization approaches on the basis of a free-vibrating beam and validated experimentally in the context of a residential-sized wind turbine blade subjected to an impulse load.

The present paper explores the application of a well-established vibration-based damage detection method to an operating Vestas V27 wind turbine blade. The blade is analyzed in a total of four states, namely, a healthy one plus three damaged ones in which trailing edge openings of increasing sizes are introduced. In each state, the blade is subjected to controlled actuator hits, yielding forced vibrations that are measured in a total of 12 accelerometers; of which 11 are used for damage detection. The dimensionality of these acceleration data is reduced by means of principal component analysis (PCA), and then a reduced set of selected principal scores are employed as damage features in the Mahalanobis metric in order to detect damageinduced anomalies. The present paper explores the application of a well-established vibration-based damage detection method to an operating Vestas V27 wind turbine blade. The blade is analyzed in a total of four states, namely, a healthy one plus three damaged ones in which trailing edge openings of increasing sizes are introduced. In each state, the blade is subjected to controlled actuator hits, yielding forced vibrations that are measured in a total of 12 accelerometers; of which 11 are used for damage detection. The dimensionality of these acceleration data is reduced by means of principal component analysis (PCA), and then a reduced set of selected principal scores are employed as damage features in the Mahalanobis metric in order to detect damage-induced anomalies.

The present paper documents a proposed modal and wavelet analysis-based structural health monitoring (SHM) method for damage identification in wind turbine blades. A finite element (FE) model of a full-scale wind turbine blade is developed and introduced to a transverse surface crack. Hereby, post-damage mode shapes are derived through modal analysis and subsequently analyzed with continuous two-dimensional wavelet transformation for damage identification, namely detection, localization and assessment. It is found that valid damage identification is obtained even when utilizing the mode shape of the first structural blade mode. However, due to the nature of the proposed method, it is also found that the accuracy of the damage assessment highly depends on the number of employed measurement points.

Laser-welded joints of stainless steel AISI304 are investigated experimentally to determine the transfor- mation of austenite to martensite during the welding process. This transformation, which occurs in the welded region due to heating and residual stresses, can influence the fatigue and fracture properties of the affected material. Therefore, the scope of the present study is to determine the quantity of introduced martensite in the welded region and hereby clarify the influence of laser welding on the fatigue and fracture properties of welded AISI304 joints. The quantification of martensite concentration is carried out by use of four different methods, namely Lichtenegger and Bloech (LB1) etching, Ferritescope, X-ray diffraction (XRD), and Vickers hardness. It is found that a concentration of 1-1.6 % martensite is introduced in the laser-welded area; a quantity that has insignificant influence on the fatigue properties of the joints.

The aim of the present paper is to evaluate structural health monitoring (SHM) techniques based on modal analysis for crack detection in small wind turbine blades. A finite element (FE) model calibrated to measured modal parameters will be introduced to cracks with different sizes along one edge of the blade. Changes in modal parameters from the FE model are compared with data obtained from experimental tests. These comparisons will be used to validate the FE model and subsequently discuss the usability of SHM techniques based on modal parameters for condition monitoring of wind turbine blades.

The stochastic dynamic damage location vector (SDDLV) method has previously proved to facilitate effective damage localization in truss- and plate-like structures. The method is based on interrogating damage-induced changes in transfer function matrices in cases where these matrices cannot be derived explicitly due to unknown input. Instead, vectors from the kernel of the transfer function matrix change are utilized; vectors which are derived on the basis of the system and state-to-output mapping matrices from output-only state-space realizations. The idea is then to convert the kernel vectors associated with the lowest singular values into static pseudo-loads and apply these alternately to an undamaged reference model with known stiffness matrix. By doing so, the stresses in the potentially damaged elements will, theoretically, approach zero. The present paper demonstrates an application of the SDDLV method for localization of structural damages in a cantilevered residential-sized wind turbine blade. The blade was excited by an unmeasured multi-impulse load and the resulting dynamic response was captured through accelerometers mounted along the blade. The static pseudo-loads were applied to a finite element (FE) blade model, which was tuned against the modal parameters of the actual blade. In the experiments, an undamaged blade configuration was analysed along with different damage scenarios, hereby testing the applicability of the SDDLV method.

Due to their inherent, ability to provide structural information on a local level, mode shapes and t.lieir derivatives are utilized extensively for structural damage identification. Typically, more or less advanced mathematical methods are implemented to identify damage-induced discontinuities in the spatial mode shape signals, hereby potentially facilitating damage detection and/or localization. However, by being based on distinguishing damage-induced discontinuities from other signal irregularities, an intrinsic deficiency in these methods is the high sensitivity towards measurement, noise. The present, article introduces a damage localization method which, compared to the conventional mode shape-based methods, has greatly enhanced robustness towards measurement, noise. The method is based on signal processing of spatial mode shapes by means of continuous wavelet, transformation (CWT) and subsequent, application of a generalized discrete Teager-Kaiser energy operator (GDTKEO) to identify damage-induced mode shape discontinuities. In order to evaluate whether the identified discontinuities are in fact, damage-induced, outlier analysis of principal components of the signal-processed mode shapes is conducted on the basis of T2-statistics. The proposed method is demonstrated in the context, of analytical work with a free-vibrating Euler-Bernoulli beam under noisy conditions.

The stochastic dynamic damage location vector (SDDLV) method utilizes the vectors from the kernel of a damaged-induced transfer function matrix change to localize damages in a structure. The kernel vectors associated with the lowest singular values are converted into static pseudo-loads and applied alternately to an undamaged reference model with known stiffness matrix, hereby, theoretically, yielding characteristic stress resultants approaching zero in the damaged elements. At present, the discrimination between potentially damaged elements and undamaged ones is typically conducted on the basis of modified characteristic stress resultants, which are compared to a pre-defined tolerance value, without any thorough statistical evaluation. In the present paper, it is tested whether three widely-used statistical pattern-recognition-based damage-detection methods can provide an effective statistical evaluation of the characteristic stress resultants, hence facilitating general discrimination between damaged and undamaged elements. The three detection methods in question enable outlier analysis on the basis of, respectively, Euclidian distance, Hotelling's statistics, and Mahalanobis distance. The study of the applicability of these methods is based on experimentally obtained accelerations of a cantilevered residential-sized wind turbine blade subjected to an unmeasured multi-impulse load. The characteristic stress resultants are derived by applying the static pseudo-loads to a representative finite element (FE) model of the actual blade.

Wind turbines are repeatedly exposed to natural loads, which, in general, have a significant influence on the structural lifetime. Therefore, maintenance and manual inspection are of great importance in the attempt to reduce catastrophic failures; both in onshore and offshore scenarios. Vibration-based structural health monitoring (SHM) has the potential to provide information about potential structural deterioration, hence allowing for efficient inspection and, as such, a reduction in operational costs. However, this requires a robust method for each step of the damage identification process, which consists of four subcategories proposed by A. Rytter [1]; namely, detection, localization, assessment and consequence. The process is performed stepwise, hence leading to that detection must be completed before locating the damage. Detecting damages in wind turbines has been solved with reasonable success [2], but a robust solution to the next step in the damage identification process, finding its location, has not been provided. A contribution to the second step is the newly developed method subspace exclusion zone (SEZ), proposed by Bernal and Ulriksen [3]. The SEZ method is a model-based damage localization approach, which facilitates a user-defined localization resolution. The method operates by mapping the damage-induced difference in the kinematic response, from an undamaged and damaged state, to a theoretical model of the structure. The SEZ method has shown promising results in the context of numerical simulations and laboratory experiments with a simple beam structure [4]. Therefore, the focus of this paper is to test the SEZ method on a more complex geometry, here, the residential-sized wind turbine blade in a laboratory environment.

Vibration-based structural health monitoring (VSHM) employs vibration signals as observables from which inferences are made concerning the integrity of structural systems. More specifically, the premise is to identify damage through changes in a set of features extracted from the vibration signals. A major challenge in this regard is that false positives may arise due to the influence of environmental and operational variabilities (EOVs). Environmental variabilities, e.g. shifts in temperature and humidity, introduce changes in mechanical properties. These changes are reflected in the vibration response and can reduce the probability of detecting damage in a structure. This paper conducts a comparative study between a novel semi-supervised damage detection approach and a well known cointegration-based scheme to deal with the variabilities induced by EOVs. The novel approach uses the pattern recognition capability of an artificial neural network (ANN) to learn how the EOVs affect a Mahalanobis distance-based damage index in a reference state. The cointegration-based scheme seeks to mitigate EOVs by computing stationary linear combinations of non-stationary output response signals. The merit of the damage detection methods are examined in the context of a mass-spring system, which is exposed to a simulated temperature field that renders output response non-stationary. The system is analysed in a reference state and a perturbed state in which damage is emulated by reducing a single spring stiffness by 2%. Although both approaches successfully mitigate the effects of EOVs, the results show that the ANN-based damage detection approach improved the damage detection accuracy. Vibration-based structural health monitoring (VSHM) employs vibration signals as observables from which inferences are made concerning the integrity of structural systems. More specifically, the premise of this work is to detect damage through changes in a set of features extracted from the vibration signals. A major challenge in this regard is that false positives may arise due to the influence of environmental and operational variabilities (EOVs). Environmental variabilities, e.g. shifts in temperature and humidity, introduce changes in mechanical properties. These changes are reflected in the vibration response and can reduce the probability of detecting damage in a structure. This paper conducts a comparative study between a novel semi-supervised damage detection approach and a well known cointegration-based scheme to deal with EOVs. The novel approach uses the pattern recognition capability of an artificialneural network (ANN) to learn how EOVs affect a Mahalanobis distance-based damage index in a reference state. The cointegration-based scheme seeks to mitigate the EOVs by computing stationary linear combinations of non-stationary output response signals. The merits of the damage detection methods are examined in the context of a mass-spring system, which is exposed to a simulated temperature field that renders the output response non-stationary. Thesystem is analysed in a reference state and a perturbed state in which damage is emulated byreducing a single spring stiffness by 2%. Both methods are evaluated with the area under thecurve (AUC) for receiver operating characteristic (ROC) and the false alarm rate. The results show that the ANN-based damage detection approach outperforms the cointegration-based one in this particular example.