Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures

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ORIGINAL PAPER

Combined approach for optimal sensor placement and experimental verification in the context of tower‑like structures Ina Reichert1   · Peter Olney2 · Tom Lahmer1 Received: 26 May 2020 / Revised: 21 September 2020 / Accepted: 22 October 2020 © The Author(s) 2020

Abstract When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures’ models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure’s behavior and model parameters without the need of preliminary measurements for model updating. Keywords  Design of experiments · Tower-like structures · Experimental validation · Mean-squared error · Fisher information matrix · Modal analysis

1 Introduction For assessing civil engineering structures, methods for designing optimal experiments (DoE) increasingly come to the fore. It often takes a lot of effort, especially in the case of tall structures, to equip the structure with the measurement devices, the associated cables and controllers. This makes it inevitable to develop a proper design for the measurement setup. In other fields like biological or chemical engineering many approaches for the DoE are well known and applied [3, 12–14]. Nowadays, measurement concepts in civil * Ina Reichert ina.reichert@uni‑weimar.de Tom Lahmer tom.lahmer@uni‑weimar.de 1



Institute of Structural Mechanics, Chair of Stochastics and Optimization, Bauhaus-Universität Weimar, Marienstr. 15, 99423 Weimar, Germany



Hillsboro 97124, Oregon, USA

2

engineering mainly arise from the engineer’s experience and the available knowledge about the structure. Usually, an equal distribution of the sensors is used when there is no further information of the structure available [5, 6, 37]. Others make use of the modal information, such as natural frequency and modeshape, to gain the optimal sensor placement [18, 28]. To improve this practice, it is useful to apply methods of DoE in order to place sensors at signi

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