The analyst can at this point select the solution on the front which better satisfies the specific problem. For the multiobjective optimization problem, the objectives are here defined by splitting the terms in equation (8) and considering each contribution separately: ( ) ( ) ∑ ∑ = = = = N i i N i i J MAC J 1 1 ; ε δ δ ω ψ (10) By choosing the two objective functions as in equation (10), the solutions in the Pareto front will result in a trade-off between the overall fit in modal frequencies and the overall fit in the mode shapes. 3. THE CART3 WIND TURBINE In this paper, the model updating methodology will be applied to the 3-bladed Control Advance Research Turbine (CART-3), located at the NREL test facility in Boulder, Colorado. This turbine is a Westinghouse model WWG-0600, modified in order to obtain a simple aerodynamic behavior and allow designers to focus on control strategies. The control laws are designed using a multibody model of the turbine [10,11]. To improve the model, a test campaign on the turbine in parked condition was performed within a collaboration between LMS International and NREL, using both Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA) techniques [12]. For a preliminary correlation and to verify the applicability of the proposed methodology, only the EMA results in terms of natural frequencies and mode shapes will be here used. The identified natural frequencies are presented in Table 1. A detailed description of the test campaign can be found in [13]. Table 1: Identified mode shapes from the Experimental Modal Analysis test campaign MODE DESCRIPTION FREQUENCY [Hz] MODE DESCRIPTION FREQUENCY [Hz] 1 Tower fore-aft 0.86 9 2nd rotor asym. flap 6.44 2 Tower side-to-side 0.88 10 2nd rotor asym. flap 6.56 3 1st rotor asym. flap 1.45 11 2nd rotor sym. flap 6.89 4 1st rotor asym. flap 1.51 12 2nd rotor asym. flap 6.96 5 1st rotor sym. flap 1.85 13 2nd tower fore-aft 7.16 6 1st rotor asym. lag 2.97 14 3rd rotor asym. flap 9.44 7 1st rotor asym. lag 3.06 15 3rd rotor asym. flap 9.89 8 2nd rotor asym. flap 4.14 (-) (-) (-) The numerical model of the wind turbine is built using the commercial multibody software LMS Virtual.Lab Motion. The model is built using rigid bodies. The connections between different components of the mechanism are modeled using rigid joints, while to model the flexibility of the tower and the blades the bodies are connected with massless elastic force elements. In this model, the Euler-Bernoulli linear beam force element available in Virtual.Lab Motion is used. According to NREL’s instructions, the tower is modeled using the data in [10]. Being the data obtained from a parked-condition test, the nacelle is rigidly connected to the tower and, together with the transmission and the electrical components, is modeled as a single rigid body. The hub, rigidly attached to the tower, is modeled also a rigid body, but its inertia contributions are kept separated from those of the nacelle. Usually, blade properties are listed in a table such as the one in [10], where all parameters are described at different locations along the pitch axis of the blade. For these specific blades, only the mass and directional stiffness properties were identified, without any detailed information about the body inertias and the gravitational and elastic centre locations. Since these parameters are mandatory to create a multibody model, an approximation is introduced and the model is built assuming the blade as a straight cantilevered beam, with the elastic and gravitational axis located along the pitch axis. The parameter identification methodology will then try to update the inertia and stiffness parameters to match the experimental results. Figure 1 shows the multibody model of the wind turbine created in Virtual.Lab Motion and figure 2 a screenshot of the mode shapes animation tool; figure 3 focuses then on the modeling of the blade, with the lumped element used to model the inertia and stiffness properties of each section. After building the model, the initial correlation between experimental and numerical model is investigated. Due to the limited number of sensors used to identify the blade dynamic behavior and the small number of bodies used to build the flexible multibody model, only the lower order modes will be used to drive the updating phase. In particular, together with the fore-aft tower bending mode (see table 1), only the 1st order flap and lag modes of the rotor are included. The tower side-to-side mode is found to be highly non-mono-phase, resulting in a complex behavior difficult to be matched; hence, it is decided not to consider it as a reference. The components of the vector which cause this behavior are the nodes on the non-vertical blades; it was verified that excluding those components, the MAC value was relatively high and the visualization of the mode satisfactory. The initial correlation between each pair of modes in terms of the indices defined in equations 6 and 7 are listed in table 2. 352
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