The modal analysis of mechanical or civil engineering structures consists of three steps: data collection, system identification and modal parameter estimation. The system identification step plays a ...crucial role in the quality of the modal parameters, that are derived from the identified system model, as well as in the number of modal parameters that can be determined. This explains the increasing interest in sophisticated system identification methods for both experimental and operational modal analysis. In purely operational or output-only modal analysis, absolute scaling of the obtained mode shapes is not possible and the frequency content of the ambient forces could be narrow banded so that only a limited number of modes are obtained. This drives the demand for system identification methods that take both artificial and ambient excitation into account so that the amplitude of the artificial excitation can be small compared to that of the ambient excitation. An accurate, robust and efficient system identification method that meets this requirements is combined deterministic–stochastic subspace identification. It can be used both for experimental modal analysis and for operational modal analysis with deterministic inputs. In this paper, the method is generalized to a reference-based version which is faster and, if the chosen reference outputs have the highest SNR values, more accurate than the classical algorithm. The algorithm is validated with experimental data from the Z24 bridge that overpassing the A1 highway between Bern and Zurich in Switzerland, that have been proposed as a benchmark for the assessment of system identification methods for the modal analysis of large structures. With the presented algorithm, the most complete set of modes reported so far is obtained.
Modal tests on large structures are often performed in multiple setups for practical reasons. Several sensors are kept fixed as reference sensors over all setups, while the other, so called roving ...sensors, are moved from one setup to another. This paper develops an optimal sensor placement strategy for multi-setup modal identification, which simultaneously optimizes the locations of the reference sensors and roving sensors. As an optimality criterion, the Information Entropy is adopted, which is a scalar measure of uncertainty in the Bayesian framework. The focus in the application goes to repetitive structures where modes typically occur in clusters, with closely spaced natural frequencies and similar wavelengths. The proposed strategy is illustrated for selecting optimal positions of uni-axial sensors for a repetitive frame structure. The influence of the number of reference sensors and two strategies for positioning roving sensors, i.e. a cluster and a uniform distribution of roving sensors, are investigated. The number of reference sensors is found to be preferably equal to or larger than the number of modes to be identified. In this case, the information content, as quantified by the Information Entropy, is not very sensitive to the roving sensor strategy. If less reference sensors are used, it is highly preferred to distribute the roving sensors uniformly over the structure instead of clustering them. The proposed strategy has been validated by an experimental modal test on a floor of an office building of KU Leuven, which has a nearly repetitive structural layout. The results show how optimally locating sensors allows extracting more information from the data. Though the focus is on applications involving repetitive structures, the proposed strategy can be applied to multi-setup modal identification of any large structure.
•A new optimal sensor placement strategy for multi-setup modal analysis is proposed.•A computationally efficient algorithm is proposed based on the BSSP algorithm.•General suggestions are made on the number of reference sensors and placement of roving sensors.•An experiment was conducted for the validation of the proposed strategy.
Vibration-based force identification of cables has been studied for several decades. Most of this work relies on the natural frequencies of the cable for an estimation of the cable force. However, ...these natural frequencies are also affected by bending stiffness, sag effect and boundary conditions. In the present work, a two-step methodology is developed that allows taking into consideration these effects in the force identification. First, a segment of the cable is considered which is sufficiently short for the sag effect to be negligible. The axial force in this segment is estimated by fitting the measured response to the analytical solution for the transverse motion of the cable in the frequency domain. In this procedure, the bending stiffness is updated exploiting the fact that the estimated axial force should not depend on the frequency, while the boundary conditions do not need to be known. Next, an analytical solution of the static state of the entire cable is derived, taking into account the sag effect, bending stiffness and boundary conditions. The parameters of the entire cable model can then be updated, using the estimated value of the axis force at the location of the segment. Finally, the updated analytical model of the entire cable allows evaluating internal forces such as the cable force and bending moment, as required for estimating the stresses in the cable considering bending deformation. The feasibility of the proposed methodology is verified by means of numerical simulations considering measurement noise and an inaccurate initial guess of the bending stiffness, proving its potential for the health monitoring of cable structures.
Quasi-periodic structures, as found in multi-span bridges, multi-bay and multi-storey buildings, are often characterized by a high modal density, even at low frequencies. This clustering of modes ...poses challenges in operational modal analysis, as well as in finite element model updating, where a pairing of experimental and numerically predicted modes is required. To overcome these difficulties, an alternative method for model updating based on the so-called free wave characteristics has recently been proposed. In this work, this method is applied to calibrate a finite element model of the K032 viaduct of the A11 highway in Bruges, Belgium. Vibration measurements are conducted to experimentally determine the free wave characteristics of the viaduct. In the model updating, the discrepancy between the calculated and identified free wave characteristics is minimized. The results are validated by comparing measured frequency response functions with those obtained from the updated finite element model.
Modal parameter estimation requires a lot of user interaction, especially when parametric system identification methods are used and the modes are selected in a stabilization diagram. In this paper, ...a fully automated, generally applicable three-stage clustering approach is developed for interpreting such a diagram. It does not require any user-specified parameter or threshold value, and it can be used in an experimental, operational, and combined vibration testing context and with any parametric system identification algorithm. The three stages of the algorithm correspond to the three stages in a manual analysis: setting stabilization thresholds for clearing out the diagram, detecting columns of stable modes, and selecting a representative mode from each column. An extensive validation study illustrates the accuracy and robustness of this automation strategy.
► A fully automated, three-stage clustering approach is developed for interpreting stabilization diagrams. ► It follows the course of a manual analysis but it does not contain parameters that need to be specified or tuned by the user. ► It only needs a single data record and it can be used with any parametric identification algorithm. ► An extensive validation study confirms its robustness and accuracy.
Many civil engineering structures have a repetitive or quasi-periodic geometry. Such structures have clustered modes with closely spaced natural frequencies corresponding to mode shapes with similar ...wavelengths. Such modes may be difficult to distinguish in modal tests and lead to difficulties when pairing calculated and experimentally determined modal characteristics in vibration-based model updating. For repetitive structures, the free wave characteristics, i.e. propagation constants and free waves, can be used alternatively to characterize their dynamic behaviour. The free wave characteristics can therefore be used instead of modal characteristics as data features in model updating of repetitive structures. This paper investigates the feasibility of model updating of repetitive structures based on free wave characteristics. First, the identification of the free wave characteristics from the measured vibration responses of a periodic structure is investigated. A stabilization diagram is constructed to pick up the stable free waves. Second, model updating of repetitive structures is performed through a match of the calculated and experimentally identified free wave characteristics. A least-squares cost function is formulated and minimized using a gradient-based optimization algorithm. This algorithm requires the sensitivity of the free wave characteristics to the model parameters that need to be updated. The analytical expressions for the free wave sensitivities are therefore derived. The proposed model updating procedure is demonstrated and validated by a numerical case study involving a repetitive frame structure and by an experiment on a four-storey steel frame structure. The results confirm the feasibility of model updating based on free wave characteristics for repetitive structures.
•A non-linear least-squares method is developed to identify free waves.•It is proposed to construct stabilization diagrams to select stable free waves.•A model updating method based on free wave characteristics is proposed.•An experiment has been conducted to verify the proposed method.
Structural health monitoring relies on the repeated observation of damage-sensitive features such as strains or natural frequencies. A major problem is that regular changes in temperature, relative ...humidity, operational loading, and so on also influence those features. This influence is in general nonlinear and it affects different features in a different way. In this article, an improved technique based on kernel principal component analysis is developed for eliminating environmental and operational influences. It enables the estimation of a general nonlinear system model in a computationally very efficient way. The technique is output-only, which implies that only the damage-sensitive features need to be measured, not the environmental parameters. The nonlinear output-only model is identified by fitting it to the damage-sensitive features during a phase in which the structure is undamaged. Afterwards, the structure is monitored by comparing the model predictions with the observed features. The technique is validated with natural frequency data from a three-span prestressed concrete bridge, which was progressively damaged at the end of a one-year monitoring period. It is demonstrated that capturing the regular variations of the features requires a nonlinear model. Monitoring the misfit between the predictions made with this model and the observed data allows a very clear discrimination between validation data in undamaged and damaged conditions.
The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of ...state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.
► The acceleration response due to each identified mode is estimated by mean of the Kalman filter. ► The contribution of the identified modes to the measured acceleration is computed. ► The modal contribution is used to select the order of the state space model. ► We propose to plot the modal contribution next to the stabilization diagram. ► The joint analysis of both plots is useful for selecting physical modes.
A method for vibration-based damage localization and quantification, based on quasi-static flexibility, is presented. The experimentally determined flexibility matrix is combined with a virtual load ...that causes nonzero stresses in a small part of the structure, where a possible local stiffness change is investigated. It is shown that, if the strain–stress relationship for the load is proportional, the ratio of some combination of deformations before and after a stiffness change has occurred, equals the inverse local stiffness ratio. The method is therefore called local flexibility (LF) method. Since the quasi-static flexibility matrix can be composed directly from modal parameters, the LF method allows to determine local stiffness variations directly from measured modal parameters, even if they are determined from output-only data. Although the LF method is in principle generally applicable, the emphasis in this paper is on beam structures. The method is validated with simulation examples of damaged isostatic and hyperstatic beams, and experiments involving a reinforced concrete free–free beam and a three-span prestressed concrete bridge, that are both subjected to a progressive damage test.
Over recent decades, the artificial neural networks (ANNs) have been applied as an effective approach for detecting damage in construction materials. However, to achieve a superior result of defect ...identification, they have to overcome some shortcomings, for instance slow convergence or stagnancy in local minima. Therefore, optimization algorithms with a global search ability are used to enhance ANNs, i.e. to increase the rate of convergence and to reach a global minimum. This paper introduces a two-stage approach for failure identification in a steel beam. In the first step, the presence of defects and their positions are identified by modal indices. In the second step, a feedforward neural network, improved by a hybrid particle swarm optimization and gravitational search algorithm, namely FNN-PSOGSA, is used to quantify the severity of damage. Finite element (FE) models of the beam for two damage scenarios are used to certify the accuracy and reliability of the proposed method. For comparison, a traditional ANN is also used to estimate the severity of the damage. The obtained results prove that the proposed approach can be used effectively for damage detection and quantification.
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