Shifei Yang

Output-Only Modal Analysis Using Continuous-Scan Laser Doppler Vibrometry and Application to a 20kW Wind Turbine

Continuous-scan laser Doppler vibrometry (CSLDV) is a method whereby one continuously sweeps the laser measurement point over a structure while measuring, in contrast to the conventional scanning LDV approach where the laser spot remains stationary while the response is collected at each point. The continuousscan approach can greatly accelerate measurements, allowing one to capture spatially detailed mode shapes along a scan path in the same amount of time that is typically required to measure the response at a single point. The method is especially beneficial when testing large structures, such as wind turbines, whose natural frequencies are very low and hence require very long time records. Several CSLDV methods have been presented that employ harmonic excitation or impulse excitation, but no prior work has performed CSLDV with an unmeasured, broadband random input. This work extends CSLDV to that class of input, developing an outputonly CSLDV method (OMA-CSLDV). This is accomplished by adapting a recently developed algorithm for linear time-periodic systems to the CSLDV measurements, which makes use of harmonic power spectra and the harmonic transfer function concept developed by Wereley. The proposed method is validated on a randomly excited free-free beam, where one-dimensional mode shapes are captured by scanning the laser along the length of the beam. The natural frequencies and mode shapes are extracted from the harmonic power spectrum of the vibrometer signal and show good agreement with the first seven analytically-derived modes of the beam. The method is then applied to identify the shapes of several modes of a 20kW wind turbine using a ground based laser and with only a light breeze providing excitation.

Two Algorithms for Mass Normalizing Mode Shapes From Impact Excited Continuous-Scan Laser Doppler Vibrometry

Continuous-scan laser Doppler vibrometry (CSLDV), a concept where a vibrometer measures the motion of a structure as the laser measurement point sweeps over the structure, has proven to be an effective method for rapidly obtaining mode shape measurements with very high spatial detail using a completely non-contact approach. Existing CSLDV methods obtain only the operating shapes or arbitrarily scaled modes of a structure, but the mass-normalized modes are sought in many applications; for example, when the experimental modal model is to be used for substructuring predictions or to predict the effect of structural modifications. This paper extends an approach based on impact excitation and CSLDV, presenting a new least squares algorithm that can be used to estimate the mass-normalized modes of a structure from CSLDV measurements. Two formulations are derived: one based on real-modes that is appropriate when the structure is proportionally damped and a second that accommodates a complex-mode description. The latter approach also gives the algorithm further latitude to accommodate time-synchronization errors in the data acquisition system. The method is demonstrated on a free-free beam, where both CSLDV and a conventional test using an accelerometer and a roving-hammer are used to find its first seven mass normalized modes. The scale factors produced by both methods are found to agree with a tuned analytical model for the beam to within about ten percent. The results are further verified by attaching a small mass to the beam and using the model to predict the change in the structure’s natural frequencies and mode shapes due to the added mass.

Harmonic Transfer Function to Measure Translational and Rotational Velocities With Continuous-Scan Laser Doppler Vibrometry

A laser Doppler vibrometer typically measures the translational velocity at a single point along the direction of incident light. However, it has been shown that rotational velocities can also be recovered by scanning the laser continuously along a line or circular path around that point. This work uses the harmonic transfer function concept, which is analogous to the transfer function in conventional modal analysis, to relate the measured rotational and translational velocities to the input force. With this concept, the continuous-scan approach can be combined with the conventional point by point scan approach, acquiring normalized translational and rotational velocities under various types of excitation conditions in the same amount of time that is required for obtaining only the translational velocity. The proposed approach is validated on measurements taken from a downhill ski under free-free boundary conditions. The influence of the circle size, the scanning rate and the surface quality on the noise level in the measured signal is discussed, and the measured deflection shapes using both the point and circular scan approaches are compared. Local slopes at measurement locations are computed from the identified principal rotational velocities, laying the foundation for constructing a much more accurate estimate of the deformation shape, which may be valuable in damage detection and/or model updating.

Modal Analysis of Rotating Wind Turbine Using Multiblade Coordinate Transformation and Harmonic Power Spectrum

Understanding and characterization of wind turbine dynamics, especially when operating, is an important though challenging task. The main problem is that an operating wind turbine cannot be truly modeled as a time invariant system, which limits the applicability of conventional well-established modal analysis methods. This paper compares two experimental techniques that characterize the dynamic behavior of an operating horizontal axis wind turbine (Vestas V27, 225 kW, rotor diameter 27 m, 12 accelerometers on each blade). The first method uses a multiblade coordinate transformation to convert the time periodic system into a time invariant one, assuming that the system is perfectly isotropic. Conventional operational modal analysis then can be applied to identify the modal parameters of the time invariant model. The second method processes the periodic response directly based on an extension of modal analysis to linear time periodic systems. It utilizes the harmonic power spectrum, which is analogous to the power spectrum for a time invariant system, to identify a periodic model for the turbine. This work demonstrates both of these methods on measurements from the operating turbine and discusses the challenges that are encountered. The procedure is demonstrated by using it to extract the time-periodic mode shapes of the first edge-wise modes, revealing that this turbine apparently has non-negligible blade-to-blade variations and hence the dynamics of these modes are considerably different than one would expect for an anisotropic turbine.

Experimental Modal Analysis on a Rotating Fan Using Tracking-CSLDV

Continuous Scan Laser Doppler Vibrometry (CSLDV) modifies the traditional mode of operation of a vibrometer by sweeping the laser measurement point continuously over the structure while measuring, enabling one to measure spatially detailed mode shapes quickly and minimizing the inconsistencies that can arise if the structure or test conditions change with time. When a periodic scan path is employed, one can decompose the measurement into the response that would have been measured at each point traversed by the laser and obtain the structure’s mode shapes and natural frequencies using conventional modal analysis software. In this paper, continuous‐scan vibrometry is performed on a rotating fan, using computer controlled mirrors to track the rotating fan blades while simultaneously sweeping the measurement point over the blades. This has the potential to circumvent the difficulty of attaching contact sensors such as strain gauges, which might modify the structure and invalidate the results. In this work, im...

Mode Shape Comparison Using Continuous-Scan Laser Doppler Vibrometry and High Speed 3D Digital Image Correlation

Experimental structural dynamic measurements are traditionally obtained using discrete sensors such as accelerometers, strain gauges, displacement transducers, etc. These techniques are known for providing measurements at discrete points. Also, a majority of these sensors require contact with the structure under test which may modify the dynamic response. In contrast, a few recently developed techniques are capable of measuring the response over a wide measurement field without contacting the structure. Two techniques are considered here: continuous-scan laser Doppler vibrometry (CSLDV) and high speed three dimensional digital image correlation (3D-DIC). The large amount of measured velocities and displacements provide an unprecedented measurement resolution; however, they both require post processing to obtain measurements. In this investigation, the frequency response function of a clamped-clamped flat beam will be determined using a modal hammer test, CSLDV, and high speed 3D-DIC. The mode shapes of the beam determined by each of these experimental methods will then be compared to assess the relative merits of each measurement approach.

Comparing Measured and Computed Nonlinear Frequency Responses to Calibrate Nonlinear System Models

Many systems of interest contain nonlinearities that are difficult to accurately model from first principles, so it would be preferable to characterize the system experimentally. For many nonlinear systems, it is now possible to measure frequency response curves with stepped sine testing and to compute frequency response curves with numerical continuation. Nonlinear frequency response curves are very sensitive to the system model and the nonlinearities and they provide a lot of insight into the response of the system to a variety of inputs. This paper explores the feasibility of a nonlinear model updating approach based on nonlinear frequency response and the experimental and analytical tools that are needed. For the experiment, a cantilever beam with an unknown nonlinearity is driven with a harmonic force at various frequencies. The steady-state response is measured and processed with the fast Fourier transform to obtain the frequency response curve. Some subtle yet important details regarding how this is implemented are discussed. An analytical model is also constructed and its frequency response computed using a recently developed technique. The measured and simulated frequencies are then compared and used to tune the analytical model.

A Lifting Algorithm for Output-only Continuous Scan Laser Doppler Vibrometry

Continuous Scan Laser Doppler Vibrometry (CSLDV) can greatly accelerate modal testing by continuously sweeping the measuring laser over the structure, effectively capturing the response of the structure at tens or even hundreds of points simultaneously. The authors recently extended this technique to the case where the input forces are unmeasured and random using harmonic power spectrum. This paper presents a variant on the proposed method that combines lifting, a resampling approach, with the output only algorithm. Lifting causes all of the peaks in the harmonic power spectrum to collapse onto a single peak for each mode, greatly simplifying modal parameter estimation. The proposed approach works by estimating and then lifting the harmonic correlation function, which is analogous to the impulse response of the system. The proposed algorithm is evaluated on a simulated beam and compared with the previous output only methods, indicating that the new approach gives comparable results to those of the previous methods but the data reduction is far simpler. The algorithm is then used to identify the first several modes of a parked wind turbine under wind excitation, capturing the deformation shape along one blade in detail. A new long range Remote Sensing Vibrometer (RSV) from PolyTec ® was employed for these measurements. This new vibrometer allows the first several modes of the turbine to be captured, from a standoff distance of 77 meters without the retro-reflective tape applied to the turbine. The speckle noise in the measurements is found to be remarkably small, allowing a 36 Hz scan frequency to be employed, which corresponds to a surface velocity of the laser spot of more than 500 m/s.

Linear and Nonlinear Response of a Rectangular Plate Measured with Continuous-Scan Laser Doppler Vibrometry and 3D-Digital Image Correlation

Dynamic measurement of real structures, such as panels, can be difficult due to their low mass and complicated deformations under large amplitude loading conditions. These conditions bring to light shortcomings of traditional sensors such as accelerometers, strain gauges, displacement transducers, etc. A majority of these sensors require contact with the structure under test which tends to modify the dynamic response of these light structures. In contrast, a few recently developed techniques are capable of measuring the response over a wide measurement field without contacting the structure, which is ideal for these structures. Two techniques are considered here: continuous-scan laser Doppler vibrometry (CSLDV) and high speed three dimensional digital image correlation (3D-DIC). Both techniques can be used to return real-time deformation shapes under certain conditions; however, measurements will be obtained using post processing here. The linear and nonlinear deformations of a clamped flat plate under steady state sinusoidal loading will be measured using both techniques and compared with a finite element model to assess the relative merits of each measurement approach.