Predicting wave load distributions using indirect methods
Introduction
Since structural health monitoring was introduced to the offshore industry in the mid 70s (Begg et al., 1976; Loland and Dodds, 1976; Nataraja, 1983), state of the art has undergone major advances. Currently, it has become industry practice to monitor offshore structures on a continuous basis. The primary reason for this monitoring is health assessment/damage detection and also estimating the fatigue damage accumulation (Augustyn et al., 2019; Tygesen et al., 2018a, 2018b; Devriendt et al., 2014; Wang et al., 2018). These are used for inspection planning and may in principle extend the operational lifetime of the structures. Since the structures often are monitored in terms of response, it is appealing to use this data to evaluate whether the loads, which the structure was designed against, is valid for the actual in-place conditions. Inverse techniques for estimating stresses, displacements or loads is frequently seen in studies of hull monitoring of vessels, (Kefal and Oterkus, 2016; Kefal and Mayang, 2018). However, the nature of the problem differs due to the boundary conditions.
Indirect methods for evaluating the wave loads (on fixed structures) are seen on a couple of occasions in the literature. For instance, Jensen et al., 1990, 1992 studied the use of ARMA models for identifying wave loads on a cantilever. They assumed that the system could be equalised as a single-degree-of-freedom system and compared the estimates with analytical results. Maes et al. (2018) studied the impulsive loads from breaking waves on a monopile. They used the joint input-state algorithm (Maes et al., 2016), and pressure sensors to locally derive the pressure distribution in the splash zone. Vigsø et al. (Vigsø et al., 2018a, 2019a; Vigsø, 2020) conducted wave flume tests where the wave load spatial distribution was estimated by merging linear wave theory with wave gauge measurements. The study, (Vigsø et al., 2019a), is based on the same experimental setup as this current paper, but it focuses on a time domain approach using a Kalman filter for real time identification. An assumed spatial distribution of the wave load is stretched to follow the wetted surface of the pile defined by wave gauge measurements. The current study presents a continuation while focusing on deriving the spatial distribution of the load using the acceleration measurements. Fallais et al. (2016) and Perisic et al. (2014) did similar research, on a monopile structure, but in a numerical framework. They assumed that the spatial distribution was a known quantity. Generally, for indirect measurements, knowing the spatial distribution is paramount to the success of recreating the input force.
This paper extends the work in indirect measurements of wave loads on offshore structures. Based on a physical experiment conducted in a wave flume at LASIF in Marseille, it is shown how the structural response can be used to derive, not only the phase and magnitude of the load, but also estimate its spatial distribution. We will analyze the response of a miniature structure with similarities to monopile structures in the North Sea. The geometry and dynamic behavior of the structure are causing interaction effects, which makes current load models such as the Morrison equation invalid. The paper will start by outlining the theory of indirect measurements, then followed by the results of direct measurements and in the end, a comparison between the estimated and the measured load will be shown. The study will focus on regular wave loading with coupling effects between the fluid and structure. The direct measurements of the load are done by pressure sensors and a load cell. Due to a limited set of sensors, the approach in mapping the pressure distribution will be based on repetitions where the pressure sensors are repositioned. Since the test focuses on regular waves, and thus the steady-state response, the variations can then be averaged to obtain the full pressure field.
Section snippets
Theory
Different approaches exist in indirect load identification, both in the frequency domain and in the time domain. Since the aim of this paper is to analyze the steady-state response, it is convenient to tackle this problem in the frequency domain. We will hence rely on one of the first known methods, which was developed for load identification for military helicopters (Giansante et al., 1982; Bartlett and Flannelly, 1979; Flannelly et al., 1977). We start out by assuming that the response from
Experimental setup
An experiment campaign was conducted in April 2018 at LASIF (Large Air-Sea Interaction Facility) in Marseille. In the wave flume, a bottom-fixed monopile structure with a box girder topside is positioned. The model, which is flexible, is characterized by having a low mass ratio and a large diameter to wavelength ratio. These combined are expected to yield interaction effects which are hard to predict through analytical methods. The literature on the experimental study of wave load distributions
Direct measurements
This section contains the methodology and results for “direct” mapping the load distribution. Recall that the purpose is to estimate the distribution through indirect methods, and hence, the outcome of this section shall be used for comparison and verification purposes.
Indirect measurements
Now we turn to the indirect estimates. This approach involves a couple of pre-steps before a result can be obtained. We start by noticing that the FRF matrix expressed by Eq. (2) is based on the structural displacements (also known as receptance or dynamic flexibility) and whilst the response is measured in terms of accelerations these must be converted to accommodate the basis of the FRF matrix. The accelerations can be converted to displacements through integration in the frequency domain.
Discussion
The estimated variation in load during an averaged wave are evaluated using three different approaches; force transducer, pressure integration and acceleration data. The estimates have similar phase and amplitude although the scatter varies. The estimated point of attack during the maximum loading is summarized in Table 3. Here we see that the loads are well in phase while deviations of % exists on the estimated point of attack. For the indirect method, it was assumed that the spatial
Conclusion and future work
In this paper, we have studied the wave load distribution from regular wave loading on a flexible structure. This study was based on the axiom that “all good comes to those who average.” A finite amount of pressure sensors was prohibiting a detailed mapping of the pressure field around the structure during the waves. This was remedied by a roving group of sensors and repetitions of the test which allowed for an averaged result. The pressure was integrated to yield a line load distribution and a
Funding
The research project is funded by the Aarhus University in collaboration with the Danish Hydrocarbon Research and Technology Center (DHRTC).
CRediT authorship contribution statement
Michael Vigsø: Conceptualization, Resources, Methodology, Software, Formal analysis, Investigation, Writing - original draft, Visualization. Christos Georgakis: Writing - review & editing, Supervision, Project administration, Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge the funding received from the Center for Oil and Gas – DTU/Danish Hydrocarbon Research and Technology Center (DHRTC). The staff from Luminy, Marseille are appreciated for their effort during the experiment campaign. Here, especially Hubert Branger and Christopher Luneau should be mentioned. Assistance from PhD students from Aarhus University should also be acknowledged. Here, the help from Thomas Kabel and Julie Kristoffersen is much appreciated.
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