1. |
__Gawlicki M.__, Jankowski Ł., *Identification of a moving load 2D path under insufficient instrumentation*,
IPM 2019, 5th International Conference on Inverse Problems Methods, 2019-05-22/05-24, Kombornia (PL), pp.1-2, **2019****Abstract:** 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.
**Keywords:** moving load identification, inverse problem, trajectory identification
**Affiliations:**
Gawlicki M. | - | IPPT PAN | Jankowski Ł. | - | IPPT PAN |
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2. |
__Gawlicki M.__, Jankowski Ł., *Identification of a load moving on a plate using the l1 norm minimization*,
SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), No.P226, pp.1-2, **2018****Abstract:** 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.
**Affiliations:**
Gawlicki M. | - | IPPT PAN | Jankowski Ł. | - | IPPT PAN |
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3. |
__Gawlicki M.__, Jankowski Ł., *Identification of moving loads using the l1 norm minimization*,
CMM 2017, 22nd International Conference on Computer Methods in Mechanics, 2017-09-13/09-16, Lublin (PL), pp.1-2, **2017****Abstract:** 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.
**Keywords:** inverse problems, structural mechanics, moving load identification, sparsity, l1 norm
**Affiliations:**
Gawlicki M. | - | IPPT PAN | Jankowski Ł. | - | IPPT PAN |
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4. |
__Gawlicki M.__, Jankowski Ł., *Identification of moving loads via l1-constrained solutions*,
ECCOMAS - IPM 2017, 4th International Conference on Inverse Problems in Mechanics of Structures and Materials, 2017-05-31/06-02, Rzeszów - Krasiczyn (PL), pp.25-26, **2017****Abstract:** 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.
**Affiliations:**
Gawlicki M. | - | IPPT PAN | Jankowski Ł. | - | IPPT PAN |
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