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Highlights • A cointegration method is proposed to deal with heteroscedastic time series in SHM. • The TBATS (T rigonometric, B ox-Cox A RMA T rend, S easonal model is used to decompose a time series corrupted with seasonal noise. • A full-scale foot bridge is presented as one of the case studies. Abstract Heteroscedasticity, or time-dependent variance, is often observed in long-term monitoring data in the context of SHM, where it is normally induced by the seasonal variations of the ambient environment. In the effort to project out the environmental and operational variations, cointegration, a method originating in econometrics, has been successfully employed in various SHM studies. This paper will explore a possible enhanced approach to cointegration, to make it applicable to heteroscedastic data. The fact that the variance of heteroscedastic data is constantly changing has a significant negative impact on conventional damage detection algorithms, making it difficult to calculate accurate confidence intervals. Thus, in the current paper, an exponential smoothing method is presented to explore and deal with the complex seasonal patterns observed in SHM time series. More specifically, in this framework, a seasonally-corrupted time series can be decomposed into three components, namely, level, seasonal and residual terms. Subsequently, the series purged of seasonality will be fed into a cointegration analysis, in order to produce a more stationary residual series (damage indicator series). Two case studies, including a synthetic case and a real world SHM dataset, are demonstrated with results and discussions. [ABSTRACT FROM AUTHOR]

High-rate systems are defined as engineering systems that undergo accelerations of amplitudes typically greater than 100 g n over less than 100 ms. Examples include adaptive airbag deployment systems, hypersonic vehicles, and active blast mitigation systems. The use of feedback mechanisms in these high-rate applications is often critical in ensuring their continuous operations and safety. Of interest to this paper are algorithms needed to support high-rate structural health monitoring (HRSHM) to empower sub-millisecond decision systems. HRSHM is a complex task because high-rate systems are uniquely characterized by (1) large uncertainties in the external loads, (2) high levels of non-stationarities and heavy disturbances, and (3) unmodeled dynamics generated from changes in system configurations that necessitate careful crafting of adaptive strategies. This paper studies benefits of integrating a data-driven predictive model with a physics-based state observer to reduce latency and convergence time estimating actionable information. The predictive model, constructed with long short-term memory (LSTM) cells, performs multi-step ahead signal prediction acting as the input to the physical model, a model reference adaptive system (MRAS). The MRAS then performs state estimation of the predicted signal rather than the true signal. A comparison study was done between the proposed hybrid algorithm and a physics-based MRAS on a testbed involving a fast-moving boundary condition. Results showed that the hybrid algorithm could perform state estimations with zero timing deadline overshoot and with up to 50% faster convergence time when compared to the MRAS under constant boundary conditions. However, the hybrid generally underperformed the MRAS algorithm in terms of convergence accuracy during motion of the boundary condition by increasing convergence time by 20%, attributable to the lag in learning the new dynamics used in predicting. The performance of the NSE algorithm was also examined on a true high-rate system, where it was shown to be capable of qualitatively tracking actionable information. • A hybrid, deep learning algorithm for real-time state estimation. • Physics-integrated algorithm with state estimation time of less than the desired sampling rate. • An algorithm with sub-millisecond computation capabilities for applications in high-rate systems. • Demonstrated performance using three case studies on experimental datasets acquired on two different testbeds. [ABSTRACT FROM AUTHOR]

Time reversal (TR) techniques due to their spatial and temporal focusing characteristics, have been increasing applied in damage evaluation. Since probing waves strongly attenuate in concrete material, imaging of damage in concrete using conventional time reversal imaging (TRI) algorithm often requires a large number of deployed transducers to minimize unexpected artifacts. To relieve economic burden and fussy installation induced by massive transducers, this paper develops a small number of transducers-enabled concrete-adapted time reversal imaging (CATRI) algorithm using implantable technology. The CATRI algorithm adopts a compensation factor to overcome wave attenuation and eliminate artifacts during crack imaging process. The implantable technology is achieved by a designed concrete implantable module (CIM) device that can be easily implanted into concrete structures. The performances of the CIM device and CATRI algorithm were numerically and experimentally studied. The results show that the proposed techniques overcome the strong wave attenuation-induced problems and successfully identify crack regions. The comparison of imaging results by using conventional TRI algorithm highlights the superiority of the CATRI algorithm for concrete crack imaging. [ABSTRACT FROM AUTHOR]

Through advances in sensor technology and development of camera-based measurement techniques, it has become affordable to obtain high spatial resolution data from structures. Although measured datasets become more informative by increasing the number of sensors, the spatial dependencies between sensor data are increased at the same time. Therefore, appropriate data analysis techniques are needed to handle the inference problem in presence of these dependencies. In this paper, we propose a novel approach that uses graphical models (GM) for considering the spatial dependencies between sensor measurements in dense sensor networks or arrays to improve damage localization accuracy in structural health monitoring (SHM) application. Because there are always unobserved damaged states in this application, the available information is insufficient for learning the GMs. To overcome this challenge, we propose an approximated model that uses the mutual information between sensor measurements to learn the GMs. The study is backed by experimental validation of the method on two test structures. The first is a three-story two-bay steel model structure that is instrumented by MEMS accelerometers. The second experimental setup consists of a plate structure and a video camera to measure the displacement field of the plate. Our results show that considering the spatial dependencies by the proposed algorithm can significantly improve damage localization accuracy. [ABSTRACT FROM AUTHOR]

The model-free hysteresis loop analysis (HLA) method for structural health monitoring (SHM) has significant advantages over the traditional model-based SHM methods that require a suitable baseline model to represent the actual system response. This paper provides a unique validation against both an experimental reinforced concrete (RC) building and a calibrated numerical model to delineate the capability of the model-free HLA method and the adaptive least mean squares (LMS) model-based method in detecting, localizing and quantifying damage that may not be visible, observable in overall structural response. Results clearly show the model-free HLA method is capable of adapting to changes in how structures transfer load or demand across structural elements over time and multiple events of different size. However, the adaptive LMS model-based method presented an image of greater spread of lesser damage over time and story when the baseline model is not well defined. Finally, the two algorithms are tested over a simpler hysteretic behaviour typical steel structure to quantify the impact of model mismatch between the baseline model used for identification and the actual response. The overall results highlight the need for model-based methods to have an appropriate model that can capture the observed response, in order to yield accurate results, even in small events where the structure remains linear. [ABSTRACT FROM AUTHOR]

Classification models are a fundamental component of physical-asset management technologies such as structural health monitoring (SHM) systems and digital twins. Previous work introduced risk-based active learning , an online approach for the development of statistical classifiers that takes into account the decision-support context in which they are applied. Decision-making is considered by preferentially querying data labels according to expected value of perfect information (EVPI). Although several benefits are gained by adopting a risk-based active learning approach, including improved decision-making performance, the algorithms suffer from issues relating to sampling bias as a result of the guided querying process. This sampling bias ultimately manifests as a decline in decision-making performance during the later stages of active learning, which in turn corresponds to lost resource/utility. The current paper proposes two novel approaches to counteract the effects of sampling bias: semi-supervised learning , and discriminative classification models. These approaches are first visualised using a synthetic dataset, then subsequently applied to an experimental case study, specifically, the Z24 Bridge dataset. The semi-supervised learning approach is shown to have variable performance; with robustness to sampling bias dependent on the suitability of the generative distributions selected for the model with respect to each dataset. In contrast, the discriminative classifiers are shown to have excellent robustness to the effects of sampling bias. Moreover, it was found that the number of inspections made during a monitoring campaign, and therefore resource expenditure, could be reduced with the careful selection of the statistical classifiers used within a decision-supporting monitoring system. [ABSTRACT FROM AUTHOR]

Abstract: A great many computational algorithms developed over the past half-century have been motivated or suggested by biological systems or processes, the most well-known being the artificial neural networks. These algorithms are commonly grouped together under the terms soft or natural computing. A property shared by most natural computing algorithms is that they allow exploration of, or learning from, data. This property has proved extremely valuable in the solution of many diverse problems in science and engineering. The current paper is intended as a tutorial overview of the basic theory of some of the most common methods of natural computing as they are applied in the context of mechanical systems research. The application of some of the main algorithms is illustrated using case studies. The paper also attempts to give some indication as to which of the algorithms emerging now from the machine learning community are likely to be important for mechanical systems research in the future. [Copyright &y& Elsevier]

This paper investigates a new probabilistic strategy for Bayesian model updating using incomplete modal data. Direct mode matching between the measured and the predicted modal quantities is not required in the updating process, which is realized through model reduction. A Markov chain Monte Carlo technique with adaptive random-walk steps is proposed to draw the samples for model parameter uncertainty quantification. The iterated improved reduced system technique is employed to update the prediction error as well as to calculate the likelihood function in the sampling process. Since modal quantities are used in the model updating, modal identification is first carried out to extract the natural frequencies and mode shapes through the acceleration measurements of the structural system. The proposed algorithm is finally validated by both numerical and experimental examples: a 10-storey building with synthetic data and a 8-storey building with shaking table test data. Results illustrate that the proposed algorithm is effective and robust for parameter uncertainty quantification in probabilistic model updating of buildings. [ABSTRACT FROM AUTHOR]

In this paper, a probabilistic multi-class pattern recognition algorithm is developed for damage monitoring of smart structures. As these structures can face damages of different severities located in various positions, multi-class classifiers are needed. We propose an original support vector machine (SVM) multi-class clustering algorithm that is based on a probabilistic decision tree (PDT) that produces a posteriori probabilities associated with damage existence, location and severity. The PDT is built by iteratively subdividing the surface and thus takes into account the structure geometry. The proposed algorithm is very appealing as it combines both the computational efficiency of tree architectures and the SVMs classification accuracy. Damage sensitive features are computed using an active approach based on the permanent emission of non-resonant Lamb waves into the structure and on the recognition of amplitude disturbed diffraction patterns. The effectiveness of this algorithm is illustrated experimentally on a composite plate instrumented with piezoelectric elements. [ABSTRACT FROM AUTHOR]

• For the first time a new population-based methodology is proposed that alleviates problems with sparsity of data in SHM. • The applicability of domain adaptation assumptions when considering each population type and SHM problem are outlined. • A novel MMD-based algorithm is proposed for an (L + 1)-problem. • A new approach for using physics-based models and domain adaption is proposed for labelling data from structures in PBSHM. • This is the third paper (of three parts) covering the foundations of population-based SHM. This is the third and final paper in a series laying foundations for a theory/methodology of Population-Based Structural Health Monitoring (PBSHM). PBSHM involves utilising knowledge from one set of structures in a population and applying it to a different set, such that predictions about the health states of each member in the population can be performed and improved. Central ideas behind PBSHM are those of knowledge transfer and mapping. In the context of PBSHM, knowledge transfer involves using information from a source domain structure, where labels are known for given feature sets, and mapping these onto the unlabelled feature space of a different, target domain structure. This mapping means a classifier trained on the transformed source domain data will generalise to the unlabelled target domain data; i.e. a classifier built on one structure will generalise to another, making Structural Heath Monitoring (SHM) cost-effective and applicable to a wide range of challenging industrial scenarios. This process of mapping features and labels across source and target domains is defined here via domain adaptation , a subcategory of transfer learning. A mathematical underpinning for when domain adaptation is possible in a structural dynamics context is provided, with reference to topology within a graphical representation of structures. Subsequently, a novel procedure for performing domain adaptation on topologically different structures is outlined. [ABSTRACT FROM AUTHOR]

The deployment of systems experiencing high-rate dynamic events, such as hypersonic vehicles, advanced weaponry, and active blast mitigation systems, require high-rate structural health monitoring (HRSHM) capabilities in the sub-millisecond realm to ensure continuous operations and safety. However, the development of high-rate feedback systems is a complex task because these dynamic systems are uniquely characterized by (1) large uncertainties in their external loads, (2) high levels of non-stationarity and heavy disturbance, and (3) unmodeled dynamics from changes in system configuration. In this paper, we present a deep learning algorithm specifically engineered for HRSHM applications. It consists of an ensemble of recurrent neural networks (RNNs) constructed with long short-term memory (LSTM) cells with transfer learning capabilities to cope with the highly limited availability of training data as it is typical for high-rate systems. The use of an ensemble of RNNs empowers multi-rate sampling capability to capture multi-temporal features of the time series, thus enabling modeling of non-stationarities. Also, because the RNNs use short-sequence LSTMs and are arranged in parallel, the computation time is substantially reduced to the sub-millisecond range. The performance of the algorithm is investigated on experimental high-rate dynamic data produced from accelerated drop tower tests and benchmarked against results from a prior investigation using a purely on-the-edge algorithm termed variable input space observer (VIO) and its hybrid architecture (hybrid VIO) that incorporated physical knowledge and is considered as an upper bound on the algorithm performance. Numerical results show that the ensemble of RNNs, composed of five RNNs, significantly outperformed the VIO, with performance close to that of the hybrid VIO when it comes to the estimation error metrics, with an average computation time of 25 μ s per prediction step. Yet, the ensemble of RNNs exhibits chattering for low-amplitude excitations, likely attributable to the behavior of RNNs sampling at small time delays. An examination of the RNN weights and hidden states confirms that the algorithm can capture multi-temporal features, and an investigation with respect to noise in the training dataset showed that the algorithm is robust for signal-to-noise ratios up to 20 dB. • Machine learning-based architecture for non-stationary time-series analysis. • Transfer learning for accelerated training with limited data. • Ensemble-based system estimation using parallel recurrent neural networks integrated with attention mechanism is proposed. • Sib-millisecond estimation of a high-rate system is achieved though the proposed architecture. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents and experimentally verifies an effective method for simultaneous identification of excitations and damages, which are two crucial factors in structural health monitoring and which often coexist in practice. The unknowns are identified by minimizing a time-domain square distance between the measured and the computed responses. Even though both damage and excitation are unknown, only damage parameters are treated here as the optimization variables: given the damage, the excitation is uniquely determined from the measured responses. As a result, all unknowns are of the same type, which allows standard optimization algorithms to be used and obviates the need for two-step procedures. The sensitivity analysis is facilitated by interpolating in each iteration the relation between structural responses and damage parameters. The numerical costs are further decreased by the fast reanalysis approach of the virtual distortion method (VDM), which is used to compute exact impulse responses of the damaged structure. The proposed methodology is verified both numerically (using a multi-span frame) and experimentally (using a cantilever beam). Stiffness-related damages and mass-related modifications are identified successfully together with the three tested types of external excitation. [Copyright &y& Elsevier]

Abstract: Statistical pattern recognition has recently emerged as a promising set of complementary methods to system identification for automatic structural damage assessment. Its essence is to use well-known concepts in statistics for boundary definition of different pattern classes, such as those for damaged and undamaged structures. In this paper, several statistical pattern recognition algorithms using autoregressive models, including statistical control charts and hypothesis testing, are reviewed as potentially competitive damage detection techniques. To enhance the performance of statistical methods, new feature extraction techniques using model spectra and residual autocorrelation, together with resampling-based threshold construction methods, are proposed. Subsequently, simulated acceleration data from a multi degree-of-freedom system is generated to test and compare the efficiency of the existing and proposed algorithms. Data from laboratory experiments conducted on a truss and a large-scale bridge slab model are then used to further validate the damage detection methods and demonstrate the superior performance of proposed algorithms. [Copyright &y& Elsevier]

Abstract: Modal strain energy has been widely utilized as a damage-sensitive feature to detect structural damage. Based on the closed-form of element modal strain energy sensitivity, a statistic structural damage detection algorithm is proposed in this paper. The method is oriented to the ambient vibration measurements where only the operational mode shapes are available. The established element damage equations are incorporated with the modal scaling factors so that the damage and modal scaling factor can be solved simultaneously. The statistic analysis is implemented to take into account the uncertainties existing in the structural model and measured structural modal parameters. The sensitivity formulas of system matrix and residual vector with respect to noise are derived. The proposed statistics based element damage equations have a compact algebraic form, which does not require a large computation time and a high storage capacity. The method is verified by a numerical simply supported beam with different assumed damage. The effects of noise and damage levels on damage detection are investigated. It is demonstrated that the proposed method can identify most likely damaged elements. [Copyright &y& Elsevier]

Abstract: In this paper, we study a design method for minimizing the total cost of a wireless sensor network (WSN) used for health monitoring of railway structures. First, we present the problem, that is to simultaneously determine the number of relays and their deployment locations, the transmission power level for each sensor and relay, and the routes for transferring sensor data to a gateway using multi-hop wireless communication. Second, we formulate this task as a mathematical programming problem, and to solve this problem, we propose a near optimal algorithm based on the Lagrangian heuristic method. Finally, we verify the effectiveness of our algorithm through computational experiments carried out using data acquired from a real WSN used for railway structural health monitoring. [Copyright &y& Elsevier]

Abstract: Time–frequency analysis, including the wavelet transform, is one of the new and powerful tools in the important field of structural health monitoring, using vibration analysis. Commonly-used signal analysis techniques, based on spectral approaches such as the fast Fourier transform, are powerful in diagnosing a variety of vibration-related problems in rotating machinery. Although these techniques provide powerful diagnostic tools in stationary conditions, they fail to do so in several practical cases involving non-stationary data, which could result either from fast operational conditions, such as the fast start-up of an electrical motor, or from the presence of a fault causing a discontinuity in the vibration signal being monitored. Although the short-time Fourier transform compensates well for the loss of time information incurred by the fast Fourier transform, it fails to successfully resolve fast-changing signals (such as transient signals) resulting from non-stationary environments. To mitigate this situation, wavelet transform tools are considered in this paper as they are superior to both the fast and short-time Fourier transforms in effectively analyzing non-stationary signals. These wavelet tools are applied here, with a suitable choice of a mother wavelet function, to a vibration monitoring system to accurately detect and localize faults occurring in this system. Two cases producing non-stationary signals are considered: stator-to-blade rubbing, and fast start-up and coast-down of a rotor. Two powerful wavelet techniques, namely the continuous wavelet and wavelet packet transforms, are used for the analysis of the monitored vibration signals. In addition, a novel algorithm is proposed and implemented here, which combines these two techniques and the idea of windowing a signal into a number of shaft revolutions to localize faults. [Copyright &y& Elsevier]

Abstract: This tutorial paper aims to introduce the topic of operational modal analysis to non-specialists on the subject. First of all, it is stressed the relevance of this experimental technique particularly in the assessment of important civil infrastructure. Then, after a synthesis of required theoretical background, three of the most powerful algorithms for output-only modal identification are presented. The several steps of these identification procedures are illustrated with the processing of data collected on a concrete arch bridge with a span of 280m. As the use of operational modal analysis in the context of structural health monitoring is a subject under active research, this theme is also introduced and briefly exemplified with data continuously recorded at the same bridge. [Copyright &y& Elsevier]

Abstract: Health monitoring and prognostics of equipment is a basic requirement for condition-based maintenance (CBM) in many application domains. This paper presents an age-dependent hidden semi-Markov model (HSMM) based prognosis method to predict equipment health. By using hazard function (h.f.), CBM is based on a failure rate which is a function of both the equipment age and the equipment conditions. The state values of the equipment condition considered in CBM, however, are limited to those stochastically increasing over time and those having non-decreasing effect on the hazard rate. The previous HSMM based prognosis algorithm assumed that the transition probabilities are only state-dependent, which means that the probability of making transition to a less healthy state does not increase with the age. In the proposed method, in order to characterize the deterioration of equipment, three types of aging factors that discount the probabilities of staying at current state while increasing the probabilities of transitions to less healthy states are integrated into the HSMM. With an iteration algorithm, the original transition matrix obtained from the HSMM can be renewed with aging factors. To predict the remaining useful life (RUL) of the equipment, hazard rate is introduced to combine with the health-state transition matrix. With the classification information obtained from the HSMM, which provides the current health state of the equipment, the new RUL computation algorithm could be applied for the equipment prognostics. The performances of the HSMMs with aging factors are compared by using historical data colleted from hydraulic pumps through a case study. [Copyright &y& Elsevier]

Abstract: Modal-based damage detection algorithms are well-known techniques for structural health assessment, but they are not commonly used due to the lack of automated modal identification and tracking procedures. Development of such procedures is not a trivial task since traditional modal identification requires extensive interaction from an expert user. Nevertheless, computational efforts have to be carefully considered. If fast on-line data processing is crucial for quickly varying in time systems (such as a rocket burning fuel), a number of vibration-based condition monitoring applications are performed at very different time scales, resulting in satisfactory time steps for on-line data analysis. Moreover, promising results in the field of automated modal identification have been recently achieved. In the present paper, a literature review on this topic is presented and recent developments concerning fully automated output-only modal identification procedures are described. Some case studies are also reported in order to validate the approach. They are characterized by different levels of complexity, in terms of mode coupling, dynamic interaction effects and level of vibration. Advantages and drawbacks of the proposed approach will be pointed out with reference to available experimental results. The final objective is the implementation of a fully automated system for vibration-based structural health monitoring of civil engineering structures and identification of adequate requirements about sensor number and layout, record duration and hardware characteristics able to ensure a reliable low-cost health assessment of constructions. Results of application of the proposed methodology to modal parameter estimation in operational conditions and during ground motions induced by the recent L’Aquila earthquake will be finally presented and discussed. [Copyright &y& Elsevier]

• Optimized analytical mode decomposition is utilized to eliminate distortion. • Adaptive wavelet transform is combined with the decomposition for the first time. • Real-time parametric identification is achieved from shake table test. Extracting useful information (damage existence, location, identification, and quantification) from measured signals for damage identification is critical in structural health monitoring, while time-varying nature of most signals often require huge efforts. In this paper, adaptive wavelet analysis AWT is first introduced as a preprocessing approach of clearer, smoother and more accurate time–frequency representation. Optimized analytical mode decomposition (AMD) is then utilized for signal component extraction, with the help of AWT for bisecting frequency determination. Examples of time-varying signals of sinusoidal function and Duffing systems are used to illustrate the advantages of the algorithm, which proves to be successful in signal decomposition. Multiple AMD (MAMD) with the optimized algorithm is then utilized together with AWT for signal decomposition and system identification of the shake table test of a 1/20-scale cable-stayed bridge model. The extracted stiffness and damping coefficients retain a preliminary indication of the damage progression during the earthquake input. [ABSTRACT FROM AUTHOR]

• An extended model-based observer (EMBO) is proposed for state estimation in hysteretic nonlinear structural systems. • The observer minimizes the state error covariance given the structure of the feedback gain. • The observer is designed to be physically realizable as a nonlinear finite element model. • The performance of the EMBO is compared to an unscented Kalman filter (UKF). • The observer is validated using data from the NEESWood full-scale shake table tests. This paper proposes a model-based observer for state estimation in nonlinear hysteretic structural systems. The observer combines a nonlinear model and response measurements to estimate the complete dynamic response of the structure of interest. The feedback gain of the observer is computed by an iterative algorithm that accounts for the nonlinearity of the system and minimizes the trace of the state error covariance matrix. The main feature of the proposed observer (and its main advantage with respect to existing nonlinear state estimators) is that it is designed to be physically realizable as a nonlinear structural model, which allows the user to benefit from modeling capabilities available in finite element solvers. The performance of the proposed observer is studied in the context of a numerical example consisting of a nonlinear chain model with a Bouc-Wen model of hysteresis subjected to a base motion; the estimation results are compared to those obtained using an unscented Kalman filter. The observer is also validated experimentally using data from a six-story full-scale benchmark wood frame building tested by the NEESWood project at the E-Defense facility in Miki, Japan. The results show the effectiveness of the proposed approach to estimate the dynamic response of large-scale structural systems exhibiting a strong nonlinear behavior. [ABSTRACT FROM AUTHOR]

• EMI signature extracting method for circular PZT is given to improve sensitivity. • A modified probability-weighted algorithm is proposed to image damage location. • Combining DCMI signatures with MPDI can promote the accuracy of damage localization. Damage localization with electromechanical impedance is a significant technique in structural health monitoring and engineering community. In this paper, a newly-developed damage localization method is presented by integrating the novel signatures extraction methodology, direct-coupled mechanical impedance (DCMI), with a modified probability-weighted function. The DCMI methodology can be utilized to extract more damage-sensitive characteristic signatures from experimentally acquired raw signatures. Then a damage indicator, root mean square deviation (RMSD), is calculated in terms of real part and imaginary part of raw and DCMI signatures. The investigation on damage location imaging with a modified probability-weighted algorithm is subsequently performed and analyzed using the aforementioned indicators. To demonstrate the effectiveness of the proposed damage localization method, a series of verification experiments are conducted on a honeycomb sandwich composite structure with the surface-mounted piezoelectric sensor array. By comparing experimental results of damage localization, it is demonstrated that combining DCMI methodology with modified probability-weighted algorithm is capable of dramatically increasing the accuracy of damage location imaging. [ABSTRACT FROM AUTHOR]