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Interpretation of stabilization diagrams using density-based clustering algorithm

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Abstract

The estimation of modal parameters is a critical requirement in structural health monitoring, damage detection, design validation, among other topics. The most prevalent methodology for manual identification is via an interpretation of a stabilization diagram. A density-based algorithm for automatically interpreting this type of diagram is proposed. The method employs three stages of interpretation. First, hard criteria are used to discard distinct spurious modes. Second, a density-based algorithm, Ordering Points to Identify the Clustering Structure (OPTICS), is used to cluster data. Finally, the modal parameters are selected taking into account the density distribution of the clustered values. Automation on the procedure is proposed, tested and applied to the vibration measurements of a building structure that has been continuously monitored since 2009. The results indicate a satisfactory interpretation, despite the low signal-to-noise ratios, the effect of induced electric noise, the low density of the sensors, different ambient conditions, and the occurrence of earthquake events.

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... Rather than manually selecting consistent poles in each consistency diagram, a very time consuming activity, automatic selection of the consistent poles was achieved using an implementation of the clustering algorithm DBSCAN. The application of DBSCAN (or derivative thereof, OPTICS) to pole selection in stabilisation diagrams is not a novel one, existing work can be found here [34]. As the performance of any given clustering technique was not the focus of this study, the decision to use DBSCAN clustering over another was arbitrary, however as a very common mode of clustering and one frequently cited in literature, it may seem the most sensible. ...
... Akin to the approach used by Boroschek and Bilbao [34], the distance metric in DBSCAN was chosen to take the following form: ...
Preprint
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Modal parameter estimation of operational structures is often a challenging task when confronted with unwanted distortions (outliers) in field measurements. Atypical observations present a problem to operational modal analysis (OMA) algorithms, such as stochastic subspace identification (SSI), severely biasing parameter estimates and resulting in misidentification of the system. Despite this predicament, no simple mechanism currently exists capable of dealing with such anomalies in SSI. Addressing this problem, this paper first introduces a novel probabilistic formulation of stochastic subspace identification (Prob-SSI), realised using probabilistic projections. Mathematically, the equivalence between this model and the classic algorithm is demonstrated. This fresh perspective, viewing SSI as a problem in probabilistic inference, lays the necessary mathematical foundation to enable a plethora of new, more sophisticated OMA approaches. To this end, a statistically robust SSI algorithm (robust Prob-SSI) is developed, capable of providing a principled and automatic way of handling outlying or anomalous data in the measured timeseries, such as may occur in field recordings, e.g. intermittent sensor dropout. Robust Prob-SSI is shown to outperform conventional SSI when confronted with 'corrupted' data, exhibiting improved identification performance and higher levels of confidence in the found poles when viewing consistency (stabilisation) diagrams. Similar benefits are also demonstrated on the Z24 Bridge benchmark dataset, highlighting enhanced performance on measured systems.
... The results of these methods depend on the accurate determination of the number of orders, and it is unknown and undetermined in the analyzed vibration segment under random ambient excitation, especially for complicated systems. So, the stabilization diagram and cluster analysis are generally resorted to explain the results and eliminate spurious modes [7,8]. Many cluster analysis approaches have been proposed to extract modal parameters from the stabilization diagram. ...
... For each noise level, 100 random tests are repeated to identify the frequency, damping, and amplitude. The tapes of filter (see (8)) in dAPES is set as dAPES = = ∕3, and that in dCAPON is set as dCAPON = = ∕6, ∕3, ∕2, respectively. The results are shown in Fig. 4. We can find that it is easy to identify frequency accurately. ...
Article
This paper proposes a 2D spectral analysis method based on damped Capon (dCAPON) and damped APES (dAPES) for structural modal parameter identification. The frequency and damping are estimated from the 2D dCAPON energy spectrum first, and then the amplitude (to construct the modal shape) corresponding to the frequency-damping point is calculated by the dAPES. The raw evenly-spaced computing grid is optimized into a banded hierarchically-refined one, greatly improving the computational efficiency. The performance of the proposed method is studied and it is investigated through the numerical and experimental data of a benchmark structure. The proposed method provides a simple and direct approach to estimating structural modal parameters, particularly for frequency and damping ratio.
... Magalhães et al. [27] applied Hierarchical clustering to a 280-m concrete arch bridge by automatically analyzing 2500 datasets for modal identification. Boroschek and Bilbao [28] introduced a Density-based clustering to automatically interpret stabilization diagram and successfully applied to a building structure. Fan et al. [29] and Zeng and Kim [19] devised self-adaptive clustering algorithms to keep training the threshold when grouping modes and analyzing datasets continuously collected on a footbridge. ...
... To the best of authors' knowledge, to date, it is very difficult to derive a general criterion to evaluate mode shape's complexity. However, MCI has been extensively used and demonstrated by many real-world applications [9,18,28]. Furthermore, from engineering practical point of view, the use of a single index, MCI, containing more information would be more convenient and feasible to perform modal analysis compared to using two indices separately, e.g., MPC and MPD, which also helps to avoid more user intervention and leads to a higher automation level of modal identification. ...
Article
Automated operational modal analysis is essential for online structural health monitoring without human intervention. It remains a challenging issue due to the need of processing a large number of datasets and the involvement of many user-specified thresholds. This paper proposes a novel automated modal identification approach based on stochastic subspace identification and variational Gaussian mixture model that involves the analysis of the stabilization diagram to automatically identify modal parameters. Two validation criteria are first adopted to eliminate the spurious modes in the stabilization diagram. A Gaussian mixture model (GMM) is then used to probabilistically classify each pole in the stabilization diagram to a specific cluster. The parameters of GMM are estimated using variational inference, giving representatives of each mode, and the optimal number of clusters is automatically determined through the Dirichlet Process. The proposed framework automatically distinguishes physical modes from spurious modes with only two verified and widely used thresholds. Results of a four-story shear and a footbridge with continuous measurements demonstrate the efficacy and robustness of the proposed approach. It shows that the proposed approach can automatically identify modal parameters with high accuracy, including weakly excited and closely spaced modes.
... Also, measurement on mode shapes is less accurate than that on frequencies. Thus, a weighting factor can reduce the inaccuracy of mode shape difference on threshold calculation (Boroschek & Bilbao, 2019). ...
... Generally, mode shape is measured with limited sensors, yielding missing components of mode shape; frequency is usually measured with an accurate level. Therefore, the use of x can reduce the effect of measurement inaccuracy of mode shapes on distance calculation (Boroschek & Bilbao, 2019). An uncertainty quantification using standard derivation is used to form a weighting matrix for Finite Element Model Updating (Yang & Lam, 2018). ...
Article
Full-text available
Automated operational modal analysis (OMA) is attractive and has been extensively used to replace traditional OMA, which requires much empirical observation and engineers’ judgment. Still, the uncertainties on modal parameters and spurious modes are challenging to estimate under the field conditions. For addressing this challenge, this research proposed an automated modal identification approach. The proposed approach consists of two steps: (1) modal analysis using covariance-driven stochastic subspace algorithm; (2) automated interpretation of the stabilization diagram. An additional uncertainty criterion is employed to initially remove as many spurious modes as possible. A novel threshold calculation for clustering is proposed with incorporating uncertainty of modal parameters and the weighting factor. An improved self-adaptive clustering with new distance calculation is used to group physical modes, followed by the final step of robust outlier detection to select outlying modes. The proposed automated approach requires minimum human intervention. Two field tests of the footbridge and a post-tensioned concrete bridge are used to verify the proposed approach. A modal tracking was used for continuously measured data for demonstrating the applicability of the approach. Results show the proposed approach has fairly good performance and be suitable for automated OMA and long-term health monitoring.
... Also, measurement on mode shapes is less accurate than that on frequencies. Thus, a weighting factor can reduce the inaccuracy of mode shape difference on threshold calculation (Boroschek & Bilbao, 2019). ...
... Generally, mode shape is measured with limited sensors, yielding missing components of mode shape; frequency is usually measured with an accurate level. Therefore, the use of x can reduce the effect of measurement inaccuracy of mode shapes on distance calculation (Boroschek & Bilbao, 2019). An uncertainty quantification using standard derivation is used to form a weighting matrix for Finite Element Model Updating (Yang & Lam, 2018). ...
Preprint
Automated operational modal analysis (OMA) is attractive and has been extensively used to replace traditional OMA, which involves much empirical observation and engineers’ judgment. However, the uncertainties on modal parameters and spurious modes are still challenging to estimate under the field conditions. For addressing this challenge, this research proposed an automated modal identification approach. The proposed approach consists of two steps: (1) modal analysis using covariance-driven stochastic subspace algorithm (SSI-cov/ref); (2) automated interpretation of the stabilization diagram. An additional uncertainty criterion is employed to initially remove as many spurious modes as possible. A novel threshold calculation for clustering is proposed with incorporating uncertainty of modal parameters and the weighting factor. An improved self-adaptive clustering with new distance calculation is used to group physical modes, followed by the final step of robust outlier detection to select outlying modes. The proposed automated approach requires minimum human intervention. Two field tests of the footbridge and a post-tensioned concrete bridge are used to verify the proposed approach. A modal tracking was used for continuously measured data for demonstrating the applicability of the approach. Results show the proposed approach has fairly good performance and be suitable for automated OMA and long-term health monitoring.
... Vibration-based structural health monitoring (SHM) techniques are being increasingly used in the structural evaluation of new structures [1][2][3][4][5][6] and historical buildings [7][8][9], such as bell towers [10][11][12], churches [13][14][15][16][17][18], and rammed earthen structures [19]. These techniques have been developed to monitor the dynamic properties of real structures with the objective of detecting structural damage [20][21][22], because modal parameters such as natural frequencies, mode shapes, and modal damping are functions of the buildings physical characteristics, such as mass, energy dissipation and stiffness [23]. ...
... where f i , n i , and / i are the natural frequency, the damping ratio, and the mode shape of an identified vibration mode, respectively; f min , f max , n min and n max are the upper and lower natural frequency and damping limits; d f k i and d n k i are the userdefined distances of natural frequency and damping between two consecutive model orders; and k1 and k2 are the maximum and minimum eigenvalues of the covariance matrix between the real and imaginary part of the modal shape [5,59]. Finally, MAC / i / j À Á and MPCi are user-defined parameters for the minimum values of the Modal Assurance Criteria and of the Modal Phase Collinearity. ...
Article
Through long-term monitoring, modal parameters identified in-situ can provide important information about the safety state of civil buildings and infrastructures. Unfortunately, structures are subjected to changing environmental conditions that can mask variations in the dynamic properties caused by damage and, therefore, lead to an incorrect condition assessment. The quantification of the influence of environmental conditions on modal parameters is a crucial step to eliminate their interference in a safety evaluation. Under current state-of-the-art considerations, this step is still an open challenge because environmental variables are time-dependent non-uniform quantities that have different influences on structural systems depending on the predominant material. In this paper, the effects of ambient temperature and humidity on the dynamic properties of earthen constructions are investigated using laboratory tests. A dynamic monitoring system was successfully implemented on adobe walls of different thicknesses to examine the influence of seasonal and daily variations of temperature and humidity. Three 1:1 scale adobe masonry walls were built and exposed to ambient conditions for 240 days. Temperature and humidity variations on the exterior, as well as in the inner walls, were continuously recorded together with the dynamic behavior using ambient vibration. The results provide useful insights on the influence of thermohygrometric parameters on the dynamic properties of adobe systems. The seasonal results indicate unclear correlations of ambient parameters and environmental variables. On the other hand, at a daily scale, the results indicate the existence of a clear relationship between inner measurements and dynamic properties. Moreover, the results indicate the existence of a delayed effect of external ambient parameters in the dynamic behavior of earthen systems.
... Covariance-driven stochastic subspace identification (SSI-Cov, Peeters and De Roeck, 1999) is applied, in combination with the OPTICS clustering algorithm (OPTICS, Ankerst et al., 1999). The approach employed is the one presented in Boroschek and Bilbao (2019). The system identification is applied to distinguish between the tower Fore-Aft (FA) and tower Side-Side (SS) direction of the wind turbine, which are obtained by transforming the local coordinates using the yaw angle provided by the SCADA data. ...
Article
Full-text available
Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers.
... This study only introduces the N4SID implementation algorithm. In order to remove spurious modes, stabilization graphs were plotted [36]. ...
Article
Full-text available
The system identification of concrete dams using seismic monitoring data can reveal the practical dynamic properties of structures during earthquakes and provide valuable information for the analysis of structural seismic response, finite element model calibration, and the assessment of postearthquake structural damage. In this investigation, seismic monitoring data of the Pacoima arch dam were used to identify the structural modal parameters. The identified modal parameters of the Pacoima arch dam, derived in different previous studies that used forced vibration tests (FVT), numerical calculation, and seismic monitoring, were compared. Meanwhile, different modal identification results using the input-output (IO) methods and the output-only (OO) identification methods as well as the linear time-varying (LTV) modal identification method were adopted to compare the modal identification results. Taking into account the different excitation, seismic input, and modal identification methods, the reasons for the differences among these identification results were analyzed, and some existing problems in the current modal identification of concrete dams are pointed out. These analysis results provide valuable guidance regarding the selection of appropriate identification methods and the evaluation of the system identification results for practical engineering applications.
... To obtain the dynamic properties of the system, the vibration signals from all accelerometers are used, in which an identification process is made using the Covariance-Driven Stochastic Subspace Identification (Cov-SSI) algorithm. The most probable value of the modal parameters is then automatically selected through a stabilization diagram using the OPTICS density base clustering algorithm, allowing to track the parameters over time (Boroschek and Bilbao 2019;González et al. 2021). This setup allows recording the dynamic properties of the system every 15 min. ...
Article
Full-text available
In Structural Health Monitoring understanding the effect of the environment on the modal properties of structures is essential. In this study, we evaluate the influence of changes in ambient conditions on the natural frequencies of three real large-scale structures: A 9-story reinforced concrete (RC) building and two sixteenth century churches of adobe masonry. For these structures, both environmental parameters (ambient temperature and relative humidity) and modal parameters were continuously monitored for a combined period of 8-years (RC building) and 2-years (for each of the adobe churches) in order to assess the effect of daily and seasonal variations of environmental parameters on the modal response. The results of the seasonal comparison indicate a negative correlation between ambient temperature and natural frequencies for the concrete structure, while for adobe structures a positive correlation between humidity and natural frequencies was observed. For daily variations, an out-of-phase and lag response of natural frequencies to variations in the environment was observed. A change on the daily lag was observed depending on the time of the year. Both seasonal and daily comparisons show the existence of a strong seasonality in frequency variations, where the form of response of this to environmental effects is different depending on the season. The magnitude of the daily variability is smaller in comparison to the seasonal variations. Finally, it was determined that the variation in natural frequencies depends on several factors such as the predominant material of the structure (namely reinforced concrete and adobe), the type of environmental exposure (temperature or humidity), and the characteristics of the structure (dimension of main elements).
... For the W27 turbine, acceleration measurements at three elevations from Acc. 1 and 2, Acc. 3, and the accelerometer in the RNA are transformed into the local RNA coordinate system to allow for separate identification of the FA and SS modes. From the stabilization diagram produced by the SSI-Cov routine, stable columns corresponding to structural modes are identified using the OPTICS clustering algorithm [52,53]. ...
Preprint
Full-text available
Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPFLM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, modeling of unknown sources of excitation as a Gaussian process (GP) serves to facilitate strain estimation by providing a complete stochastic characterization of the covariance relationship between input forces and states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch-Tung-Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands.
... The identification is made with stabilization diagrams generated with the SSI-COV algorithm [46]. The automatic interpretation of these diagrams is done with the algorithm proposed in [47], based on the OPTICS clustering algorithm [48]. The real-time acquisition of modal frequencies, i.e., the modal tracking, is done with the MAT (Model Assisted Tracking) algorithm proposed in [33]. ...
Article
For Civil Engineering System Structural Health Monitoring (SHM), damage identification is typically based on the observation of appropriate response features. A commonly selected feature is the variation of modal frequency due to its high sensitivity to global damage. However, this parameter also has a high sensitivity to variables unrelated to damage, such as the weather and the structure’s usage. This article focuses on the application of Recurrent Neural Networks (RNN) with Long-Short Term Memory (LSTM) blocks to modal tracking in medium-rise buildings, a case study for which there is very little literature despite being one of the most common building types in urban areas. RNN with LSTM blocks are trained to characterize the environmental trend in the modal frequency to identify the most critical variables and to develop models than can be used to detect changes of state or damage. The models are fed with the recent history of the external temperature, sun position and the modal frequency itself. The performance of these models is evaluated in two different ways: for a variable size of the training set of real data and for scenarios with segments in which the modal response is not known at all instants, a typical situation in real structures. A practical application of this approach in a real medium-rise building is presented, showing that these models are capable of capturing with high precision the annual evolution of the modal frequency and performing well even on a daily scale, making it suitable for damage detection. For the cases in which the modal response is regularly identified and tracked, the characterization has a high performance when tracking single modal frequency or several frequencies with a single model. The models are robust for periods where data is not available but quickly deteriorate if this period extends for several days.
... In addition, selecting a larger minPts is recommended for cases involving large volumes or severe noise contaminants in a dataset. Boroschek and Bilbao (2019) suggested that the optimal minPts is 1/3 of the total number of modal orders. ...
Article
The recent development of automated operational modal analysis (OMA) has enabled the modal tracking of environmental and operational conditions. Variations in these conditions have prevented investigations into the long-term characteristics of the damping ratio due to its inherently high degree of scattering. In this study, the long-term damping characteristics of a twin cable-stayed bridge under environmental and operational variations were investigated. A displacement reconstruction algorithm was applied to resolve the model-order dependency in OMA-based damping estimates. In order to automatically establish groups of modal estimates, optimal parameters for a density-based unsupervised clustering algorithm were proposed on the basis of gaps between target modal frequencies. The proposed clustering parameters were first validated by comparing the clustering results with those of manually determined ground truth classes. Next, the applicability of the clustering parameters for long-term damping estimation was demonstrated by quantifying the dispersion of modal estimates in each cluster. Subsequently, the framework was applied to 2.5 years of monitoring data to evaluate the long-term damping characteristics of the twin cable-stayed bridge that is often subjected to high variations in environmental and operational conditions. The following aspects are mainly discussed: (1) seasonal fluctuation in long-term damping ratios; (2) the effect that aerodynamic interference exerts on variations in the dynamic characteristics; and (3) the amplitude dependency of the damping ratio. The probability distribution of the modal damping ratio is provided based on the statistical analysis of reliable modal damping ratios.
... As a result, the Modal Parameter Extraction (MPE) has been almost completely automatized, even if still some statistical rules must be established for defining the threshold value to cut the hierarchical tree and, subsequently, forming the clusters. Moreover, other studies proposed some histogram analysis, dividing the stable poles into narrow bins [17,27] or using a density-based clustering algorithm [28]. Recently, a two-stage Dirichlet Process Gaussian Mixture Model (DP-GMM) algorithm has been proposed in [29] to tackle the clustering phase. ...
Article
Many efforts have been made in the last decade to define Automated Operational Modal Analysis (AOMA) procedures able to process large datasets from long-term monitoring systems. However, some issues are still open and further studies on this topic are needed; in particular following points should be better investigated: i) controlling the tuning parameters to minimize the modelling errors, ii) defining suitable automatization method for processing large datasets and iii) validating the extracted modal parameters. These points are investigated in this paper with the aim of enhancing the current AOMA procedures based on the Stochastic Subspace Identification (SSI) techniques, and the following novelties are introduced: i) a minimization approach for the tuning of the initial parameters in the SSI algorithm, ii) a statistical method to automatically define the cut-off threshold in the hierarchical clustering phase, and iii) a Modal Quality Index (MQI) – ranging from 0 to 1 – to validate the identified modes. The above novelties represent key aspects that allow a real-time check of the modal parameters provided by a monitoring system within a Continuous Structural Health monitoring (CSHM) framework.
... There are different algorithms for different clustering models; some of the clustering models are as follows: Connectivity model [42], Centroid models [43], Distribution models [44], Density models [45], and Neural models [46]. Ease of use and high calculation speed make neural models efficient in comparison with other models. ...
Article
Full-text available
With progressive advances in the synthesis, characterization, and commercialization of nanoparticles and nanomaterials, these modern engineered materials are becoming an ingredient of innovative structural materials for various applications in civil and construction engineering. In this research, MgO nanoparticles were systematically added to normal concrete samples in order to investigate the effect of these nanomaterials on the durability of the samples under freeze and thaw conditions. The compressive and tensile strengths as well as the permeability of concrete samples containing nanoparticles were measured and compared with the corresponding values of control samples without nanoparticles. The curing time of the concrete samples, the amount of nanoparticles, and the water-cement ratios ( w / c ) were the variables of the experiments. Moreover, data clustering and the Charged System Search (CSS) algorithm were utilized as the numerical analysis and optimization methods. The regression analysis before clustering and after clustering proved the process of clustering is a prerequisite of regression analysis. Furthermore, the CSS optimization method showed that the optimum amount of nano MgO is 1% of the weight of cement, which can increase the compressive strength of concrete by 9.12% more than plain samples over 34 days.
... In addition, selecting a larger minPts is recommended for cases involving large volumes or severe noise contaminants in a dataset. Boroschek and Bilbao (2019) suggested that the optimal minPts is 1/3 of the total number of modal orders. ...
Preprint
Full-text available
The recent development of automated operational modal analysis (OMA) has enabled the modal tracking of environmental and operational conditions. Variations in these conditions have prevented investigations into the long-term characteristics of the damping ratio due to its inherently high degree of scattering. In this study the long-term damping characteristics of a twin cable-stayed bridge under environmental and operational variations was investigated. A displacement reconstruction algorithm was applied to resolve the model-order dependency in OMA-based damping estimates. In order to automatically establish groups of modal estimates, optimal parameters for a density-based unsupervised clustering algorithm were proposed on the basis of gaps between target modal frequencies. The proposed clustering parameters were first validated by comparing the clustering results with those of manually determined ground-truth classes. Next, the applicability of the clustering parameters for long-term damping estimation was demonstrated by quantifying the dispersion of modal estimates in each cluster. Subsequently, the framework was applied to 2.5 years of monitoring data to evaluate the long-term damping characteristics of the twin cable-stayed bridge that is often subjected to high variations in environmental and operational conditions. The following aspects are mainly discussed: (1) seasonal fluctuation in long-term damping ratios; (2) the effect that aerodynamic interference exerts on variations in the dynamic characteristics; and, (3) the amplitude dependency of the damping ratio. The probability distribution of the modal damping ratio is provided based on statistical analysis of reliable modal damping ratios.
... N4SID needs fewer parameters for tuning), the N4SID method is being considered for the SWS. Also, the use of Bayesian and clustering analysis techniques, described in Boroschek and Bilbao (2019) and Zonno et al. (2018), are also being explored for future implementation in the proposed SWS. ...
Article
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The seismic response of an instrumented 22-story rehabilitated building is presented. The building analyzed is as part of a complex (called CCUT) with three low-rise structures and a common basement founded on soft soil that was built in 1964. Since it was under construction until date, the building tower has experienced differential settlements and tilting. To mitigate such problems, the building has been subjected to several rehabilitations over the years. During the 1985 and 2017 high-intensity earthquakes in Mexico City, the tower suffered some damage. The aim of this article is to discuss the structural health monitoring system implemented for the tower and to describe the structure’s performance since the last rehabilitation in 2009. A monitoring methodology designed and implemented as a structural warning system based on five structural health indicators, two on seismic severity and three on structural performance, to automatically process seismic records, is presented. The results of the seismic response of the CCUT tower between 2011 and 2018 indicate that the structure had suffered moderate damage. Analysis of data, corroborated by building inspection, confirmed that the structure exhibited good performance during the 19 September 2017 Puebla-Morelos earthquake. The importance of the information obtained from the structural warning system is highlighted as a promissory tool for establishing a robust decision framework for occupants’ safety.
... System identification is performed using the SSI-COV algorithm [26]. The automatic interpretation of the stability diagram is performed using the algorithm proposed and validated in [27] based on the Ordering Points To Identify the Clustering Structure (OPTICS) clustering algorithm [28]. Fig. 4 shows the result of the identification performed with 15-min windows for the entire period of analysis (2011)(2012)(2013)(2014)(2015)(2016)(2017). ...
Article
In Structural Health Monitoring (SHM), the instrumentation policies for buildings usually require large numbers of high-resolution sensors. The relatively high economic cost for the sensors and their interconnecting cables has discouraged the widespread application of SHM. For modal analysis, small number of sensors means low spatial resolution of mode shapes, which limits the possibility of differentiating between close frequency modes in a single measurement and between consecutive measurements on a continuous monitoring system. In this study, we try to overcome this limitation, particularly on the tracking component of SHM, with the aid of a predictive numerical model based on the effect of the ambient temperature on the modal frequency. To validate this hypothesis, we test it on a real building, monitored with a small number of low-resolution sensors. The methodology’s performance is evaluated during normal conditions, rainfall and also after the damaging Chile Maule earthquake (Mw of 8.8), proving to be effective for tracking purposes. For this building, the sensitivity of the mode shape and damping to the environment is also studied, showing a very low sensitivity as compared to the frequency. This validates the simpler temperature – frequency model.
... Among them, one of the most essential parameters is the model order n, which is the minimum number of state variables required to represent a system. The stabilization diagram has been recognized as a robust tool to estimate the optimal model order, which is a plot figured by model orders and modal parameters identified at each of these orders including modal frequency, damping ratio and mode shape [47][48][49][50]. To do so, a sufficiently wide range of model orders are examined. ...
Article
The stochastic subspace identification (SSI) method has been recognized as the most dominant and popular system identification technique in the time domain. Nevertheless, it cannot cope with the non-synchronicity of dynamic response measurements that happens sometimes in structural health monitoring practice. To overcome this, this study proposes a strategy for the SSI algorithm to realize system identification from non-synchronous dynamic response measurements. The modal identification is carried out in a pairwise manner by pairing a time-shifted signal with a common reference signal. The state space model is employed to fit the pair of reference and time-shifted signals and the SSI algorithm is exploited to extract the modal parameters. The core of the strategy is the tactical usage of the mean phase deviation (MPD) of the mode for seeking out the actual time lag as well as the actual mode shape components simultaneously. By so doing, the strategy fulfills integrated time lag estimation and modal extraction for non-synchronous dynamic response measurements. Furthermore, the strategy also overcomes the difficulty to determine the model order with the use of the stabilization diagram and reduces the computational cost substantially with the help of the periodicity of the MPD. To examine the performance of the strategy, intensive validations are conducted by making use of the non-synchronous acceleration measurements of the Jiangyin Bridge subjected to a ship collision and the artificially misaligned acceleration measurements of the Canton Tower struck by an earthquake. Both the time lags and the mode shapes identified by the strategy can be well validated, indicating that the proposed strategy is competent for modal identification of non-synchronous dynamic response measurements.
... Recently, a lot of research effort has been focused on extracting the modal responses via on-line modal analysis methods [6][7][8][9][10][11]. Commonly, to assist in identifying modes, it is possible to try and locate the peaks of a frequency response function. ...
... In terms of the automated modal identification procedures based on SSI, the automation processes mainly contribute to reducing the user intervention in modal analysis, especially in the interpretation of the SSI output to select the physical modes from the stabilization diagram. [11][12][13][14][15] The major challenge for the automated OMA procedures is to distinguish the physical modes and spurious modes from a number of observed modes in the stabilization diagram. To address this challenge, clustering techniques including hierarchical clustering and K-means clustering, which can be used to group the physical modes across various system model orders into the same clusters, are several of the most popular methods to automatically interpret the SSI output and select the physical modes. ...
Article
A robust automated method for operational modal analysis (OMA) is in a great demand for processing a large amount of structural health monitoring data from engineering structures. This paper proposes an improved automated OMA approach based on data‐driven Stochastic Subspace Identification (SSI) and clustering techniques with novel criteria. The framework of the proposed approach includes two main components, namely, “modal identification by SSI” and “automated interpretation of SSI output.” Three procedures including hard validation criteria removal, an improved statistics‐based clustering procedure, and a developed cluster merging procedure are combined in the second component for automatically interpreting the stabilization diagram from the SSI output, without a priori knowledge on the modal parameters and no manual tuning during interpreting. Numerical validation results on a frame structure model demonstrate that the proposed approach is capable of identifying the vibration modes accurately, under a significant noise effect. No spurious modes are observed, and the physical modes can be accurately identified. Experimental studies on a steel frame structure in the laboratory and a real footbridge are conducted to demonstrate the robustness and applicability of using the proposed approach for automated OMA and modal tracking. Identification results are compared with baselines and those from an existing reference method to demonstrate the improvement and contribution made in the proposed approach on the automated OMA.
... The system identification considers 15 minutes windows without overlap, from April 8, 2011 to December 31, 2016. The identification algorithm, proposed in [3], is an automatic interpretation of stabilization diagrams based on OPTICS [4]. The stability diagrams generated with the SSI-COV algorithm [5]. ...
Article
Estimating modal parameters requires significant user interaction, especially when parametric system identification methods are used and the physical modes are selected in the stabilization diagram. In this paper, a fast density peaks clustering algorithm combined with the covariance‐driven stochastic subspace identification method is used to automatically identify modal parameters. Before the automatic identification process, the spurious modes from the stochastic subspace identification method were eliminated by a two‐stage method, including using the soft and hard verification criteria to remove spurious modes in the first stage and the removal of spurious modes based on the stability of physical modes in the second stage; thus, a better stabilization diagram was obtained for the subsequent automatic identification. Furthermore, fast density peaks clustering algorithm was applied to select the appropriate structure modes from the stabilization diagram. In the entire identification process, no user participation was required. The proposed method was demonstrated on a 4‐degree of freedom (DOF) numerical model and a benchmark frame structure, and the results indicated that the modal parameters can be identified accurately even with the noise effects using the default user‐defined parameters. This method showed higher efficiency and universality than the existing methods. Finally, the applicability and robustness of the proposed method in automated operational mode tracking were verified on a real cable‐stayed bridge.
Chapter
Fatigue assessment in offshore wind turbine support structures requires the monitoring of strains below the mudline, where the highest bending moments occur. However, direct measurement of these strains is generally impractical. This paper presents the validation of a virtual sensing technique based on the Gaussian process latent force model for dynamic strain monitoring. The dataset, taken from an operating near-shore turbine in the Westermeerwind Park in the Netherlands, provides a unique opportunity for validation of strain estimates at locations below the mudline using strain gauges embedded within the monopile foundation.
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The “Infante D. Henrique” bridge is a concrete arch bridge, with a span of 280 m that crosses the Douro River, linking the cities of Porto and Gaia located in the North of Portugal. This structure is being monitored by a recently installed dynamic monitoring system that comprises 12 acceleration channels. This paper describes the bridge structure, its dynamic parameters identified with a previously developed ambient vibration test, the installed monitoring equipment and the software that continuously processes the data received from the bridge through an Internet connection. Special emphasis is given to the algorithms that have been developed and implemented to perform the online automatic identification of the structure modal parameters from its measured responses during normal operation. The proposed methodology uses the covariance driven stochastic subspace identification method (SSI-COV), which is then complemented by a new algorithm developed for the automatic analysis of stabilization diagrams. This new tool, based on a hierarchical clustering algorithm, proved to be very efficient on the identification of the bridge first 12 modes. The results achieved during 2 months of observation, which involved the analysis of more than 2500 datasets, are presented in detail. It is demonstrated that with the combination of high-quality equipment and powerful identification algorithms, it is possible to estimate, in an automatic manner, accurate modal parameters for several modes. These can then be used as inputs for damage detection algorithms.
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Automatic operational modal analysis: challenges and practical application to a historical bridge
  • Cabboi