Institute of Fundamental Technological Research

Moving load is a fundamental loading pattern for many civil engineering structures and machines. This paper proposes and experimentally verifies an approach for indirect identification of 2D trajectories of moving loads. In line with the "structure as a sensor" paradigm, the identification is performed indirectly, based on the measured mechanical response of the structure. However, trivial solutions that directly fit the mechanical response tend to be erratic due to measurement and modeling errors. To achieve physically meaningful results, these solutions need to be numerically regularized with respect to expected geometric characteristics of trajectories. This paper proposes a respective multicriterial optimization framework based on two groups of criteria of a very different nature: mechanical (to fit the measured response of the structure) and geometric (to account for the geometric regularity of typical trajectories). The state-of-the-art multiobjective genetic algorithm NSGA-II is used to find the Pareto front. The proposed approach is verified experimentally using a lab setup consisting of a plate instrumented with strain gauges and a line-follower robot. Three trajectories are tested, and in each case the determined Pareto front is found to properly balance between the mechanical response fit and the geometric regularity of the trajectory.

structural health monitoring (SHM), moving load, trajectory identification, geometric regularity, multicriterial optimization, load identification, inverse problems, structural mechanics

This contribution presents and tests experimentally a nonparametric approach for indirect identification of 2D paths of moving loads, based on the recorded mechanical response of the loaded structure. This is an inverse problem of load identification. The method to be proposed is based on multicriterial optimization with two complementary criteria. The first criterion is purely mechanical, and it quantifies the misfit between the recorded mechanical response of the structure and its predicted response under a given trajectory. The second criterion is geometric: it represents the heuristic knowledge about the expected geometric regularity characteristics of the load paths (such as related to linear and angular velocity), and in fact it can be considered to be a regularizing criterion. A multicriterial genetic search is used to determine and advance the Pareto front, which helps to strike the balance between the response fit and the geometric regularity of the path. The proposed approach is tested in an experimental laboratory setup of a plate loaded by a line-follower robot and instrumented with a limited number of strain gauges.

moving load, trajectory identification, inverse problem, structural health monitoring, multicriterial optimization

This contribution presents an approach for indirect identification of the 2D path of a moving load. A multicriterial formulation is proposed, where one objective function quantifies the mismatch between the measured and the simulated structural response. The second objective function expresses the natural expectation that the paths of moving loads are continuous and relatively smooth, and it expresses thus a certain spline-based measure of the geometric regularity of the path. The Pareto front is determined in a local evolutionary search and used to strike the balance between the response fit and the geometric regularity of the path. The approach is tested in a laboratory experimental setup of a plate loaded by a line-follower robot. It is found that the implementation of the smoothness-based objective has a regularizing influence on the identification results: it reveals and emphasizes the actual geometrical character of the identified paths.

Trajectory Identification, Moving Load, Inverse Problem, Structural Health Monitoring, Multicriterial Optimization

This contribution deals with the inverse problem of indirect identification of moving loads. The identification is performed based on the recorded response of the loaded structure and its numerical model. A specific feature of such problems is a very large number of the degrees of freedom (DOFs) that can be excited and a limited number of available sensors. As a result, unless the solution space is significantly limited, the identification problem is underdetermined: it has an infinite number of exact, observationally indistinguishable solutions. We propose an approach based on the assumption of sparsity of the excitation, which can be expressed in the form of a requirement of a bounded l1 norm of the solution. As long as the loads are sparse, the approach allows them to be freely moving, without the usual assumption of a constant velocity. We first test the approach in a numerical example with 10% rms measurement noise. A good qualitative agreement of the numerical results allows to proceed with experimental investigations, and the moving load identification is then carried out based on the response measured experimentally on a lab test stand.

This contribution is devoted to the problem of indirect identification of 2D trajectories of moving loads based on the measured mechanical responses of the loaded structure. This is an inverse problem of load identification, and such problems have been intensively studied. Such problems are typically characterized by (1) a very large number of structural degrees of freedom that can be excited by the moving load and (2) a limited number of sensors that are used to measure the response. In effect, the na¨ıve formulation based on minimization of the residuum norm is underdetermined, and the corresponding identification problem has an infinite number of exact solutions. Thus, in order to guarantee the uniqueness of the solution, the generality of the load is typically limited by assuming that the trajectory of the moving load is known (most often, the problem is reduced to the case of a single vehicle moving over a 1D bridge at a constant velocity) and that only the magnitude of the load is subject to identification. In contrast, our aim here is to identify more general loads, and in particular trajectories of loads that are freely moving on 2D structures like plates.

moving load identification, inverse problem, trajectory identification

There are two fundamental inverse problems in the field of structural health monitoring (SHM): identification of damages and identification of loads. Effectiveness of the related computational methods is crucial for maintaining integrity of the monitored structures. This contribution considers identification of unknown loads based on measurements of structural response. It is a relatively extensively researched problem: reviews of techniques used for off-line load identification can be found in [1,2], while techniques for online identification are reviewed in [3].
If the aim is to identify independent force histories in each of the excited degrees of freedom (Dofs), the uniqueness of the solution can be possible only if there are at least as many sensors (equations) as the excited Dofs (unknowns). Such a requirement can be satisfied in case of a few unknown stationary loads, but it becomes problematic if the unknown load is (even single but) moving in an unknown way across the structure. In such a case, a very large number of Dofs can be potentially excited and a limited number of sensors are available to measure the response. As a result, the naïve direct formulation of the inverse problem is underdetermined, and the solution is not unique.
This contribution is devoted to indirect identification of a single moving load that excites a 2D structure (plate). To attain the uniqueness, the solution space needs to be significantly constrained. However, instead of assuming a known trajectory of the load and identifying its value, the aim is to identify the trajectory only. Such a problem is important, e.g., in traffic monitoring and control [4,5]. Effectively, the approach is based on the assumption of sparsity of the excitation, which seems to suit the practice: even if the location of the load is unknown, at each time instant only a single (or a limited number of) Dofs is excited. Such an approach follows the methodology of compressed sensing [6], which includes such SHM-related applications as identification of impact load position [7]. The assumption of sparsity is usually expressed as a requirement of a bounded l1 norm of the solution [8].
The approach has already been verified numerically and experimentally using a flexible 1D structure (a beam) excited with a moving mass [9]. The cases considered there included single or multiple passes of the mass across the beam. The assumption of sparsity allowed the space-time trajectory of the load to be identified. Here, the goal is to test the approach in a much more complex problem that involves a 2D structure, e.g., a plate, subjected to a single moving load. In the fully dynamic case the task is computationally very demanding, thus we focus here on the quasi-static case. This abstract describes briefly the method and the experimental stand. Detailed results will be presented during the conference.

This contribution deals with the inverse problem of indirect identification of moving loads. The identification is performed based on the recorded response of the loaded structure and its numerical model. A specific feature of such problems is a very large number of the degrees of freedom (DOFs) that can be excited and a limited number of available sensors. As a result, unless the solution space is significantly limited, the identification problem is underdetermined: it has an infinite number of exact, observationally indistinguishable solutions. We propose an approach based on the assumption of sparsity of the excitation, which can be expressed in the form of a requirement of a bounded l1 norm of the solution. As long as the loads are sparse, the approach allows them to be freely moving, without the usual assumption of a constant velocity. We test the approach in a numerical example with 10% rms measurement noise and describe an experimental setup that is being prepared to perform experimental verification.

inverse problems, structural mechanics, moving load identification, sparsity, l1 norm

Indirect identification of moving loads based on the measured response is one of the crucial problems in structural health monitoring. It is important in automated assessment of structures and pavements, in traffic monitoring and control, and as a prerequisite for structural control. As such, it has been intensively researched. An important difficulty is that a moving load can excite a very large number of structural Dofs, which all have to be taken into account in the identification procedure based on measurements of a much more limited number of sensors. A straightforward formulation yields thus an underdetermined problem with an infinite number of solutions. Therefore, in most of the approaches so far, the solution space is significantly limited by the assumption that the load corresponds to a single vehicle moving at a constant velocity, which excludes loads of a more general nature (e.g., multiple loads). However, instead of limiting the solution space, it can be noted that in practice moving loads are sparse in time and space, which fits the framework of compressed sensing. Such an a priori knowledge of sparsity is typically expressed by limiting the l1 norm of the solution. To our knowledge, although used in other contexts, the concept has not been applied so far for identification of moving loads. The approach is tested in a numerical example with 10% rms measurement noise. Experimental work is in progress.