• International Journal of Fluid Machinery and Systems
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• v.2 no.4
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• pp.278-285
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• 2009

Operational modal analysis (OMA) allows modal parameters, such as natural frequencies and damping, to be estimated solely from data collected during operation. However, a main shortcoming of these methods resides in the evaluation of the accuracy of the results. This paper will explore the uncertainty and possible variations in the estimates of modal parameters for different operating conditions. Two algorithms based on the Least Square Complex Exponential (LSCE) method will be used to estimate the modal parameters. The uncertainties will be calculated using a Monte-Carlo approach with the hypothesis of constant modal parameters at a given operating condition. In collaboration with Andritz-Hydro Ltd, data collected on two different stay vanes from an Andritz-Hydro Ltd Francis turbine will be used. This paper will present an overview of the procedure and the results obtained.

• Smart Structures and Systems
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• v.17 no.2
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• pp.209-230
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• 2016

The Canton Tower is a high-rise slender structure with a height of 610 m. A structural health monitoring system has been instrumented on the structure, by which data is continuously monitored. This paper presents an investigation on the identified modal properties of the Canton Tower using ambient vibration data collected during a whole day (24 hours). A recently developed Fast Bayesian FFT method is utilized for operational modal analysis on the basis of the measured acceleration data. The approach views modal identification as an inference problem where probability is used as a measure for the relative plausibility of outcomes given a model of the structure and measured data. Focusing on the first several modes, the modal properties of this supertall slender structure are identified on non-overlapping time windows during the whole day under normal wind speed. With the identified modal parameters and the associated posterior uncertainty, the distribution of the modal parameters in the future is predicted and assessed. By defining the modal root-mean-square value in terms of the power spectral density of modal force identified, the identified natural frequencies and damping ratios versus the vibration amplitude are investigated with the associated posterior uncertainty considered. Meanwhile, the correlations between modal parameters and temperature, modal parameters and wind speed are studied. For comparison purpose, the frequency domain decomposition (FDD) method is also utilized to identify the modal parameters. The identified results obtained by the Bayesian method, the FDD method and a finite element model are compared and discussed.

• Smart Structures and Systems
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• v.17 no.3
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• pp.445-470
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• 2016

In this study, the Bayesian probabilistic framework is investigated for modal identification and modal identifiability based on the field measurements provided in the structural health monitoring benchmark problem of an instrumented cable-stayed bridge named Ting Kau Bridge (TKB). The comprehensive structural health monitoring system on the cable-stayed TKB has been operated for more than ten years and it is recognized as one of the best test-beds with readily available field measurements. The benchmark problem of the cable-stayed bridge is established to stimulate investigations on modal identifiability and the present paper addresses this benchmark problem from the Bayesian prospective. In contrast to deterministic approaches, an appealing feature of the Bayesian approach is that not only the optimal values of the modal parameters can be obtained but also the associated estimation uncertainty can be quantified in the form of probability distribution. The uncertainty quantification provides necessary information to evaluate the reliability of parametric identification results as well as modal identifiability. Herein, the Bayesian spectral density approach is conducted for output-only modal identification and the Bayesian model class selection approach is used to evaluate the significance of different modes in modal identification. Detailed analysis on the modal identification and modal identifiability based on the measurements of the bridge will be presented. Moreover, the advantages and potentials of Bayesian probabilistic framework on structural health monitoring will be discussed.

• Structural Monitoring and Maintenance
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• v.5 no.3
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• pp.379-390
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• 2018

In this paper, a novel and effective damage diagnosis algorithm is proposed to detect and estimate damage using two stages least squares support vector machine (LS-SVM) and limited number of attached sensors on structures. In the first stage, LS-SVM1 is used to predict the unmeasured mode shapes data based on limited measured modal data and in the second stage, LS-SVM2 is used to predicting the damage location and severity using the complete modal data from the first-stage LS-SVM1. The presented methods are applied to a three story irregular frame and cantilever plate. To investigate the noise effects and modeling errors, two uncertainty levels have been considered. Moreover, the performance of the proposed methods has been verified through using experimental modal data of a mass-stiffness system. The obtained damage identification results show the suitable performance of the proposed damage identification method for structures in spite of different uncertainty levels.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.485-499
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• 2012

Mode shape expansion is useful in structural dynamic studies such as vibration based structural health monitoring; however most existing expansion methods can not consider the modelling errors in the finite element model and the measurement uncertainty in the modal properties identified from vibration data. This paper presents a reliable approach for expanding mode shapes with consideration of both the errors in analytical model and noise in measured modal data. The proposed approach takes the perturbed force as an unknown vector that contains the discrepancies in structural parameters between the analytical model and tested structure. A regularisation algorithm based on the Tikhonov solution incorporating the L-curve criterion is adopted to reduce the influence of measurement uncertainties and to produce smooth and optimised expansion estimates in the least squares sense. The Canton Tower benchmark problem established by the Hong Kong Polytechnic University is then utilised to demonstrate the applicability of the proposed expansion approach to the actual structure. The results from the benchmark problem studies show that the proposed approach can provide reliable predictions of mode shape expansion using only limited information on the operational modal data identified from the recorded ambient vibration measurements.

• Structural Monitoring and Maintenance
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• v.3 no.4
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• pp.349-375
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• 2016

The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.375-391
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• 2012

This paper reports the structural health monitoring benchmark study results for the Canton Tower using Bayesian methods. In this study, output-only modal identification and finite element model updating are considered using a given set of structural acceleration measurements and the corresponding ambient conditions of 24 hours. In the first stage, the Bayesian spectral density approach is used for output-only modal identification with the acceleration time histories as the excitation to the tower is unknown. The modal parameters and the associated uncertainty can be estimated through Bayesian inference. Uncertainty quantification is important for determination of statistically significant change of the modal parameters and for weighting assignment in the subsequent stage of model updating. In the second stage, a Bayesian model updating approach is utilized to update the finite element model of the tower. The uncertain stiffness parameters can be obtained by minimizing an objective function that is a weighted sum of the square of the differences (residuals) between the identified modal parameters and the corresponding values of the model. The weightings distinguish the contribution of different residuals with different uncertain levels. They are obtained using the Bayesian spectral density approach in the first stage. Again, uncertainty of the stiffness parameters can be quantified with Bayesian inference. Finally, this Bayesian framework is applied to the 24-hour field measurements to investigate the variation of the modal and stiffness parameters under changing ambient conditions. Results show that the Bayesian framework successfully achieves the goal of the first task of this benchmark study.

• Smart Structures and Systems
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• v.21 no.6
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• pp.727-740
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• 2018

Tuned mass dampers (TMDs) are passive damping devices widely employed to mitigate the pedestrian-induced vibrations on footbridges. The TMD design must ensure an adequate performance during the overall life-cycle of the structure. Although the TMD is initially adjusted to match the natural frequency of the vibration mode which needs to be controlled, its design must further take into account the change of the modal parameters of the footbridge due to the modification of the operational and environmental conditions. For this purpose, a motion-based design optimization method is proposed and implemented herein, aimed at ensuring the adequate behavior of footbridges under uncertainty conditions. The uncertainty associated with the variation of such modal parameters is simulated by a probabilistic approach based on the results of previous research reported in literature. The pedestrian action is modelled according to the recommendations of the Synpex guidelines. A comparison among the TMD parameters obtained considering different design criteria, design requirements and uncertainty levels is performed. To illustrate the proposed approach, a benchmark footbridge is considered. Results show both which is the most adequate design criterion to control the pedestrian-induced vibrations on the footbridge and the influence of the design requirements and the uncertainty level in the final TMD design.

• Smart Structures and Systems
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• v.17 no.3
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• pp.471-489
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• 2016

Modal identification based on ambient vibration data has attracted extensive attention in the past few decades. Since the excitation for ambient vibration tests is mainly from the environmental effects such as wind and traffic loading and no artificial excitation is applied, the signal to noise (s/n) ratio of the data acquired plays an important role in mode identifiability. Under ambient vibration conditions, certain modes may not be identifiable due to a low s/n ratio. This paper presents a study on the mode identifiability of an instrumented cable-stayed bridge with the use of acceleration response data measured by a long-term structural health monitoring system. A recently developed fast Bayesian FFT method is utilized to perform output-only modal identification. In addition to identifying the most probable values (MPVs) of modal parameters, the associated posterior uncertainties can be obtained by this method. Likewise, the power spectral density of modal force can be identified, and thus it is possible to obtain the modal s/n ratio. This provides an efficient way to investigate the mode identifiability. Three groups of data are utilized in this study: the first one is 10 data sets including six collected under normal wind conditions and four collected during typhoons; the second one is three data sets with wind speeds of about 7.5 m/s; and the third one is some blind data. The first two groups of data are used to perform ambient modal identification and help to estimate a critical value of the s/n ratio above which the deficient mode is identifiable, while the third group of data is used to perform verification. A couple of fundamental modes are identified, including the ones in the vertical and transverse directions respectively and coupled in both directions. The uncertainty and s/n ratio of the deficient mode are investigated and discussed. A critical value of the modal s/n ratio is suggested to evaluate the mode identifiability of the deficient mode. The work presented in this paper could provide a base for the vibration-based condition assessment in future.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.459-476
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• 2017

Interval valued intuitionistic fuzzy sets (IVIFSs) is widely used to model uncertainty, imprecise, incomplete and vague information. In this paper, newly defined modal operators over an extensional generalized interval valued intuitionistic fuzzy sets ($GIVIFS_Bs$) are proposed. Some of the basic properties of the new operators are discussed and few theorems were proved. The actual contribution in this paper is to discuss ten operators on $GIVIFS_Bs$.