INTRODUCTION
BACKGROUND STUDY
SHM in offshore structures
SHM and damage detection techniques are widely used in the field of civil and offshore wind turbine structures to reduce renovation costs, extend operational life and prevent catastrophic failure [1]. Structural health monitoring is emerging and is being applied in both newly built complex structures and outdated structures. The application of SHM to offshore structures is important because these structures are of great value to the economy and are built in a harsh environment.
Typically, offshore structures are subject to strong wind and tidal currents, which provide them with a harsh environment. Additionally, offshore structures that are built over oceans make them inaccessible for frequent maintenance and renovation.
Virtual sensing
In addition to this load, seawater leads to material degradation and the lack of a strong foundation can lead to failure. When a virtual detection algorithm is used in combination with an existing SHM unit, it improves the robustness of the monitoring. Frequent adjustment or replacement of sensors is not necessary because the virtual detection algorithm can estimate the response of unmeasured locations.
In addition to sensor failure, huge and complex offshore structure leads to large sensor network and inaccessible critical locations. Virtual sensor engineering helps to reduce the number of sensors used, which ultimately reduces the size of the sensor network. Thus, using virtual sensing is inevitable to improve the robustness and reliability of the SHM system.
Kalman filter
- Random variables
- Kalman filter (state estimator)
In the case of non-stationary random input, the mean of the input history is non-zero. Despite the usefulness of response estimation, it has not been fully explored in the literature. Both the input forces and the structural responses have a slowly varying trend with large amplitude depending on the changing direction of the tidal current.
The Kalman filter provides a computationally efficient means of estimating the state of a process in a way that minimizes the mean squared error. For the four types of response combinations, the best combination is obtained by assessing the accuracy of the estimated responses. Young's modulus and density of the material were chosen to be 206 GPa and 7580 kg/m3 respectively.
The originally developed numerical model was used in MATLAB Simulink to simulate the acceleration, strain and angular displacement responses of the beam under a non-stationary random input, shown in Figure 4.3, and applied to node 18. The result is consistent with the fact that given acceleration in the simulation does not contain the quasi-static behavior of the measured structure. To investigate the consistency of the virtual detection method based on the Kalman filter, the voltage responses were estimated for all locations.
The disagreement between the FRFs clearly shows the justification of an inaccurate numerical model used for response estimation. Among the multimetric Cases, Case 3 could not estimate exact quasi-static response, while Case 4 resulted in the estimated strain with better agreement with the measured strain due to lower noise level of the tilt sensor than strain gauges in practice. Note that the RMSEs in Case 3 are slightly larger than those in Case 1 at several elements, in contrast to the RMSEs in the numerical simulation shown in Fig.
Four frame elements on top of the columns have Young's modulus and density of 210 GPa and 7850 kg/m3. The developed numerical model was used in MATLAB Simulink to simulate the acceleration and load responses under a non-zero mean input. Four simulation cases are considered here, in each case one of the load responses is estimated using other load and acceleration responses. Strain gauges were placed on each column at 150 mm from the root of the specimen.
Since the important structural components of the offshore structures are located underwater, the virtual sensing strategy can be a powerful alternative to the direct measurement, especially when the structural responses are desired at locations where no sensors are present. The numerical simulation was performed with the finite element model of the small-scale offshore structure. The virtual sensing strategy has the potential to capture structural responses of the bottom-attached offshore structures under the non-stationary random tidal flow.
The assumption of Gaussian distribution for random variables is also one of the limitations of this virtual sensing technique.
DATA FUSION APPROACH FOR NON-STATIONARY RANDOM INPUTS
NUMERICAL AND EXPERIMENTAL VALIDATION
Validation with simply supported beam
- Numerical validation
- Experimental validation
In this section, a numerical model of a simply supported beam is discussed to estimate the deformation responses from limited measurements using a modified Kalman state estimator. The beam consists of 20 Euler-Bernoulli beam elements, each with a length of 0.1 m, as shown in the figure. Disturbance in the new model is introduced by changing the modulus of elasticity and the moment of inertia.
To verify the virtual sensor performance, four types of measurements are considered as shown in the figure. Thus, case 4, whose measurement has lower noise, is less affected by the model error in the estimation than the other cases, as shown in the figure. This shows that the virtual registration method has the robustness to the model error that is compensated for using the measurements.
4.6(b), Case 2 using only acceleration data has poor agreement with the exact strain in the low-frequency region below the first peak frequency, which reveals the failure to capture the quasi-static trend in strain. 4.6(a)) has relatively good agreement near 0 Hz, has a higher noise level compared to the reference. Note that the RMSEs of Case 2 were quite large compared to the others due to the inaccurate estimation of the quasi-static strain component, and therefore they were not plotted together.
The section describes the laboratory scale experiment for response estimation designed to replicate the numerical simulation. Similar to the numerical simulation, all cases estimated the strain response at the unmeasured node with some accuracy, except Case 2. 4.10(a)) resulted in the estimated stress with high noise level, while the multimetric cases (i.e. Case 3) and Case 4 ) have lower noise levels (see Figures.
Note that the peak at 60 Hz in the measured strain is from electrical noise around the laboratory where the experiment was performed. First, unlike the reference strain used in the numerical simulation, the measured strain to be used as a reference contains high noise level represented by the flatness in the anti-resonant regions. This is evidence why the strain was contaminated by higher levels of noise than the other responses in the numerical simulation.
4.11(b) clearly shows that Case 2 has poor agreement in the low frequency region (near 0 Hz) related to quasi-static component of deformation compared to other methods. Note that the RMSEs of Case 2 are much larger than the others due to imprecise quasi-static stress components, and thus they are not plotted together.
Validation with model of bottom fixed offshore structure
- Numerical validation
- Experimental validation
Using numerical model, a transition matrix of deformation to the input force is constructed. To estimate input covariance, strain at unmeasured location is assumed to be the same as nearest available strain response. In addition to the comparison in the time domain, the estimated and measured strain responses are compared in the frequency domain by plotting their power spectra as shown in Figure.
4.16, it can be observed that the estimated strain agrees well with the reference strain. The experiment is carried out in 3 steps: Step 1: Initially the embankment is filled with a water level of 400mm by closing the sluice gate at the end of the water channel (see Figure. 4.18. From the experimental deformation response it can be observed that first 60 sec the water is still and after 60 sec current velocity increases rapidly to 130 sec.
The strain gauges must be deployed perpendicular to the bending plane, otherwise the measured responses may not be accurate. The voltage and tilt response contributes to the low frequency, large amplitude trend in the estimation, while the acceleration with good high frequency information is able to reduce the random noise. The virtual sensing strategy was shown to successfully find a deformation response using the other three deformations and the acceleration on the top plate.
Acceleration was found to be inadequate to estimate the quasi-static trend of the non-zero mean strain response excited by the non-zero mean input due to the lack of accuracy in low frequency measurement near 0 Hz. The combined use of different types of measurements (i.e. strain and acceleration) can help to improve the estimation in the lower and higher frequency ranges. Based on the findings in this dissertation, further studies may include the use of the estimated response for SHM purposes such as fatigue assessment and damage detection.
-varying spectrum estimation of offshore structure response based on a time-varying autoregressive model", J Fatigue lifetime estimation in structures using environmental vibration measurements", Proceedings of the ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece, June Multi-rate Kalman Filtering for the Data Fusion of Displacement and Acceleration Response Measurements in Dynamic System Monitoring", Mech. 2014), "Operational Vibration-Based Response Estimation for Offshore Wind Lattice Structures", Proceedings of the International Modal Analysis Conference. of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No. 00EX373).
CONCLUSION, LIMITATION AND FUTURE SCOPE
ACKNOWLEDGEMENT
