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The statistical subspace-based damage detection technique has shown promising theoretical and practical results for vibration-based structural health monitoring. It evaluates a subspacebased residual function with efficient hypothesis testing tools, and has the ability of detecting small changes in chosen system parameters. In the residual function, a Hankel matrix of Output covariances estimated from test data is confronted to its left null space associated to a reference model. The hypothesis test takes into account the covariance of the residual for decision making. Ideally, the reference model is assumed to be perfectly known without any uncertainty, which is not a realistic assumption. In practice, the left null space is usually estimated from a reference data set to avoid model errors in the residual computation. Then, the associated uncertainties may be non-negligible, in particular when the available reference data is of limited length. In this paper, it is investigated how the statistical distribution of the residual is affected when the reference null space is estimated. The asymptotic residual distribution is derived, where its refined covariance term considers also the uncertainty related to the reference null space estimate. The associated damage detection test closes a theoretical gap for real-world applications and leads to increased robustness of the method in practice. The importance of including the estimation uncertainty of the reference null space is shown in a numerical study
and on experimental data of a progressively damaged steel frame.
This work describes a vibration-based structural health monitoring of a prestressed-concrete box girder bridge on the A100 Highway in Berlin by applying statistical pattern recognition technique to a huge amount of data continuously collected by an integrated monitoring system during the period from 2000 to 2013. Firstly, the general condition and potential damage of the bridge is described. Then, the dynamic properties are extracted from 20 velocity sensors. Environmental variability captured by five thermal transducers and traffic intensity approximately estimated by strain measurements are also reported. Nonlinear influences of temperature on natural frequencies are observed. Subsequently, the measurements during the first year are used to build a baseline health index. The multiple linear regression (MLR) method is used to characterize the nonlinear relationship between natural frequencies and temperatures. The Euclidean distance of the residual errors is calculated to build a statistical health index. Finally, the indices extracted from the following years gradually deviate; which may indicate structural deterioration due to loss of prestress in the prestressed tendons.
Repair is an indispensable part of the maintenance of structures over their lifetimes. Structural grouting is a widely used remediation technique for concrete components, trenches, mine subsidence, dam joints, restoration of masonry structures, and geological stabilizations. A structural grout system should be injectable in narrow spaces and hence include ingredients with finer particles. Ultrafine cements are ideal for these type of demanding grouts due to their superior properties compared to that of the less expensive, but coarser ordinary Portland cement (OPC). Supplementary cementitious materials (SCMs) are often used to replace OPC clinker based binder in order to modify certain properties and to reduce costs. The most commonly used SCMs are fly ash (FA), and ground granulated blast furnace slag (GGBS). For various special applications microsilica (MS), and metakaolin (MK) are also used. Identifying the optimum replacement contents of OPC by SCMs are a challenge during the design of such grouts. The aim of this experimental study is to investigate the effect of the selected SCMs (FA, MS and MK) on the slump flow, time of efflux, viscosity, shrinkage, and compressive and flexural strength of ultrafine cement based grouts with constant water-binder ratio and superplasticizer content. The test program was formulated using Box-Behnken design principles. Maximum percentages of replacement with ultrafine cement was 6% by volume of cement for MS and 16% for FA, and MK. The results suggest that most investigated grouts have the potential to be used for structural applications. The appropriate quadratic models are then formulated through statistical tools and presented as response surfaces. The trends indicate that fly ash improves the rheological properties, whereas microsilica and metakaolin positively affect shrinkage and mechanical properties to some extent. Based on the influence of SCMs and priorities among the properties, Decision Matrix Analysis (DMA) is carried out to select the most suitable ones among the SCMs. The analysis suggests that microsilica and fly ash are more suitable as SCMs than metakaolin without affecting the properties.
The vehicle–track interaction generates forces and consequently vibrations in the environment. The interaction has been analysed by the simultaneous measurements of vehicle, track and ground vibrations during test runs with varied train speeds. The special effects of the passage over a bridge and through a tunnel are studied and compared with the measurements on a conventional ballasted surface line. The maximum amplitudes, narrow band and one-third octave band spectra are presented for the axle-box accelerations and for the track, bridge and ground vibrations. The different frequencies and frequency bands are related to wheel out-of-roundness, track alignment errors, the sleeper passage and the wheelset–track resonance. An axle impulse component has been observed at the track, at the near-field soil and as a scattered version in the far field. Specific results can be found for the bridge track, where clearly speed-dependent bridge resonances occur due to the axle sequence of the train, and for the tunnel track where soft rail pads are responsible for a strong amplification around the wheelset–track resonance. On the other hand, the axle impulses are strongly reduced by the tunnel track, and the scattered axle impulse component is not as relevant as for the surface track. As a consequence, a strong mid-frequency amplitude reduction of the tunnel compared to the surface line has been measured for low and high train speeds by the Federal Institute of Material Research and Testing (BAM) and by other institutes.
Train-induced ground vibrations are all generated by the vehicle, by static or dynamic vehicle loads. The most important and most accepted excitation are the dynamic wheel loads from the passage over track irregularities. Dynamic wheel loads will be compared from parallel axle-box and ground vibration measurements at more than seven sites. Some low-frequency excitation of ground vibrations, typically between 10 and 30 Hz, cannot be found in the axle-box measurements. Therefore, other vehicle modes, such as rigid bogie modes, flexible carriage modes, rigid and flexible wheelset modes, have been analysed for additional excitation forces. These vehicle dynamics analyses give an explanation for higher axle-box results at high frequencies, but not for the excitation of the higher low-frequency ground-vibration component. Finally, the effect of the moving static train loads will be analysed. For a regular track and soil, the moving static train loads yield the quasi-static response which exists only in the low-frequency nearfield of the track. If the support stiffness is randomly varying along the track, the pulses on the track generate an additional low-frequency component which is called the irregular pulse responses.
This component will be demonstrated by numerical analysis where all axle pulses are superposed in frequency domain.
Many measurements of train induced ground vibrations show high amplitudes for a certain mid-frequency range. This ground vibration component cannot be well explained by dynamic loads of the train. Many characteristics indicate that the axle impulses, which are scattered by an irregular soil, are the excitation. This new understanding of railway-induced ground vibration is verified by numerical analysis. The response of the regular homogeneous and irregular inhomogeneous soils has been calculated by the finite-element method in frequency domain. A specific superposition of the impulse responses has been invented including time shift, axle sequence, track filter and hanning filter. The superposition yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil of which the stiffness varies randomly in space, the superposition yields a mid-frequency ground vibration component from the scattering of the axle impulses. The existence and the importance of this component can thus be demonstrated by the calculations. Some rules of the influence of distance, train speed, soil stiffness, strength and width of the stiffness variation have been derived from the calculations. Many measurements show the unique explanation of the mid-frequency ground vibration component by the scattered axle impulses.
Damage detection and localization in civil or mechanical structures is a subject of active development and research. A few vibration‐based methods have been developed so far, requiring, for example, modal parameter estimates in the reference and damaged states of the investigated structure, and for localization in addition a finite element model. For structures in operation, temperature has been shown to be a major nuisance to the efficiency of such methods because the modal parameters are varying not only with damage but also due to temperature variations. For detection, a few rejection approaches have been developed. Besides the increased complexity, environmental variation is hardly taken into account in localization approaches. In this paper, we propose a sensitivity‐based correction of the identified modal parameters in the damaged state with respect to the temperature field in the reference state, on the basis of a sensitivity analysis with respect to temperature dependent Parameters of the finite element model in the reference state. The approach is then applied to the stochastic dynamic damage locating vector method, where its improved performance under nonuniform temperature variations is shown in a numerical application on a beam.
The Perfectly Matched Layer (PML) method is an efficient approach to imposing radiation conditions at the bounded region of interest in case of wave propagation in unbounded domains. This paper presents and validates 3D FE/PML numerical schemes based on two different PML formulations for homogeneous and inhomogeneous geological media exhibiting discrete or continuous inhomogeneity. In the equation of motion for the PML domain the applied stretching behavior is expressed either as complex material properties or as complex coordinates. Both PML formulations are implemented in the FEM and verified against analytical solutions. Three different types of material inhomogeneity are considered: layered half-space, continuously inhomogeneous half-space with linear velocity profile and continuously inhomogeneous half-space with nonlinear velocity profile. Sensitivity analyses are conducted, and the performance of the developed numerical schemes is investigated taking into account a broad variation of the PML parameters. Recommendations are given for the optimal values of the PML parameters for the case of homogeneous and inhomogeneous geological media.