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Abstract:
Measurements of displacements of bridges under dynamic load are particularly difficult in the case of structures where access to the area under the tested structure is impossible. Then, remote measurement methods are preferred, such as interferometric radar. Interferometric radar has high accuracy when measuring displacement in the direction of its target axis. The problems appear when a bridge vibrates in two directions: horizontal (lateral or longitudinal) and vertical. The use of one radar to measure those vibrations may be impossible. This paper presents the application of a set of two interferometric radars to measure vertical vibration and horizontal longitudinal vibration with high accuracy. The method was positively verified by experimental tests on two railway bridges characterized by different levels of horizontal displacement. The accuracy of the radar measurements was tested by the direct measurement of vertical displacements using inductive gauges. In conclusion, in the case of vertical displacement measurements using one interferometric radar, the influence of horizontal displacements should be excluded. In the case of locating radars at the area of bridge supports, it is necessary to either use a set of two radars or first investigate the magnitude of possible horizontal displacements in relation to vertical displacements.

Keywords:
bridge monitoring, interferometric radar, remote measurements, dynamic vertical and horizontal displacements

Abstract:
This paper proposes a computationally effective framework for load‐dependent optimal sensor placement in large‐scale civil engineering structures subjected to moving loads. Two common problems are addressed: selection of modes to be monitored and computational effectiveness. Typical sensor placement methods assume that the set of modes to be monitored is known. In practice, determination of such modes of interest is not straightforward. A practical approach is proposed that facilitates the selection of modes in a quasi‐automatic way based on the structural response at the candidate sensor locations to typical operational loads. The criterion used to assess sensor placement is based on Kammer's Effective Independence (EFI). However, in contrast to typical implementations of EFI, which treat the problem as a computationally demanding discrete problem and use greedy optimization, an approach based on convex relaxation is proposed. A notion of sensor density is applied, which converts the original combinatorial problem into a computationally tractable continuous optimization problem. The proposed framework is tested in application to a real tied‐arch railway bridge located in central Poland.

Keywords:
optimal sensor placement, effective independence method, Fisher information matrix

Abstract:
In the case of the monitoring of bridges, the determination of vertical displacements is one of the most important issues. A new measuring system has been developed and implemented for assessment of railway bridges based on measurements of the structural response to passing trains. The system uses inertial sensors: Inclinometers and accelerometers that do not need any referential points. The system records signals related to the passage of a train over a monitored bridge. The signals from inclinometers before the train's entry are used to determine the static movement. Integrated signals from inclinometers and accelerometers are used to determine dynamic displacements when the train goes through the bridge. Signals from inclinometers are used to determine the so-called "quasi-static" component of the displacement and signal from the accelerometer to determine the dynamic component. Field tests have been carried out on a viaduct along a high-speed railway line. Periodic comparative measurements are carried out using a Total Station to verify static measurements and using inductive sensors to verify dynamic measurements. Tests of the system carried out so far have proven its usefulness for monitoring bridges in a high-speed railway (up to 200 km/h) with high accuracy while determining dynamic displacements.

Keywords:
bridge monitoring, dynamic and static displacements, inertial sensors, total station, indirect measurement

Abstract:
The methodology for optimal single-type sensor placement has been extensively discussed in the literature. However, little attention has been devoted to the distribution of multi-type sensors. The application to large structures, such as bridges or towers, poses a significant challenge. Some responses, for example, the displacements of a bridge over a river, cannot be easily measured directly. Consequently, indirect techniques can be employed to estimate the deflections of such structures. In this contribution, a Kalman filter-based algorithm is presented to address this sensor placement problem. The effectiveness of the proposed method is numerically demonstrated using the example of an actual tied-arch bridge.

Keywords:
sensors, optimal sensor placement, Kalman filter, reduced order model, arch bridge

Abstract:
The article presents the railway bridge structures monitoring system, which takes advantage of the dynamic response measurement and evaluation method. The monitoring system is focused on steel structures with the spans exceeding 30 m. The elaboration of the method which uses inclinometers together with an accelerometer for indirect displacement measurement under the dynamic load is the main achievement of the project.

Keywords:
monitoring, railway bridges, inclinometer, accelerometer

Abstract:
In practice, the broadly used finite element (FE) models can have very large number of degrees of freedom (DOFs). A small subset of DOFs representing sensor locations that provides an extremum of a selected objective function corresponding to a metric of the expected measurement accuracy is sought. Thus, optimal sensor placement is characterized by its complex combinatorial nature and tremendous computational effort required. With the aid of convex relaxation, the proposed approach allows one to transform the original combinatorial problem into its continuous counterpart, which requires smaller computational effort – by a few orders of magnitude than famous Effective Independence method. The effectiveness of the method has been demonstrated using an example of a FE model of an existing railway bridge. First, the FE model has been calibrated with measured responses of the bridge under the moving load of a passing train. Then, sensor layout has been obtained in such a way that it optimises the estimate of modal coordinates of the mode shapes participating most significantly in the measured structural response. The authors acknowledge the support of the National Science Centre, Poland (grant agreement 2018/31/B/ST8/03152).