The identification of operational modal parameters of a wind turbine blade is fundamental for online damage detection. In this paper, we use binocular photogrammetry technology instead of traditional contact sensors to measure the vibration of blade and apply the advanced stochastic system identification technique to identify the blade modal frequencies automatically when only output data are available. Image feature extraction and target point tracking (PT) are carried out to acquire the displacement of labeled targets on the wind turbine blade. The vibration responses of the target points are obtained. The data-driven stochastic subspace identification (SSI-Data) method based on the Kalman filter prediction sequence is explored to extract modal parameters from vibration response under unknown excitation. Hankel matrixes are reconstructed with different dimensions, so different modal parameters are produced. Similarity of these modal parameters is compared and used to cluster modes into groups. Under appropriate tolerance thresholds, spurious modes can be eliminated. Experiment results show that good effects and stable accuracy can also be achieved with the presented photogrammetry vibration measurement and automatic modal identification algorithm.

Modal analysis of a wind turbine blade is a key step for analysis and testing of the dynamic performance of blade structure and is also fundamental for blade design and manufacturing [

On the contrary, the stochastic subspace identification (SSI) is a classical time-domain method to identify modal parameters for a linear system directly from structural vibration response data [

From the analysis of pole discrimination above, we find that it is complex and time-consuming for the state decomposition method or inaccurate and limited scenarios with certain criterions in the stabilization diagram method and still need high skilled manipulations. In this paper, a new method of dynamics detection and automatic modal parameter identification is proposed. Photogrammetry is used to measure marked points vibration, and modal analysis is carried out with data-driven stochastic subspace identification (SSI-Data). Considering the impact of noise on vibration data, spurious modes are discriminated through reconstructing Hankel matrix multiple times and fuzzy clustering method. The modal similarity is calculated and differentiated by a new index based on tolerance and modal confidence. The modal parameters are clustered and automatically identified with statistical analysis of results from dynamic vibration sequences.

Figure

Stereo imaging model of binocular vision.

Taking the left camera as an example, the camera coordinate system is

The right camera coordinate system is

Transformation of the 3D world coordinate system to the left camera coordinate system can be described using 3 × 3 orthogonal matrix

Equation (

According to the mapping relationship between computer pixel coordinates and three-dimensional world coordinates, the world coordinates of space point

The object movements are captured by using a binocular vision system. And the dynamic images are treated with segmentation and identification. The authors developed a kind of tracking and matching technology for coded targets pasted on the blade [

After the measurement of binocular vision, the vibration data are used to identify the operational modal parameters. The measured vibration is discrete time series data. Here, we assume that the excitation is white noise with zero mean value (if the input contains dominant frequency components, these frequencies will appear as poles of the equation (

The discrete SSI model of the structure can be described as follows [

The vibration response data of multiple locations are gathered in a block Hankel matrix

By taking the QR-factorization of the Hankel matrix which consisted of

From equation (

The projection of row space of

By applying singular value decomposition (SVD) to the projection matrix,

The projection matrix can be factorized as the product of the observability matrix and the Kalman filter sequence:

Combining equations (

The matrixes

If the row space of

And we have

Defining matrix

System matrixes A and C can be obtained by solving the set of equations in least squares sense.

System state matrix

At the process of the modal parameters identification, the maximal model order

In order to verify the validity and reliability of our method, the vibration measurement experiment of a 3 kW wind turbine blade model was carried out, and the modal parameters were identified based on the measured vibration response data. Two Dahua A5131MU210 industrial cameras were selected to form a stereo camera station (Figure

Experiment configuration.

Blade images taken by using the cameras: (a) left camera and (b) right camera.

The coordinates of the targets on the image plane can be extracted from the image. The three-dimensional coordinates of the object can be obtained by solving the correspondence problem with the point tracking (PT). Then, the spatial coordinate changes of the same target point can be calculated through 1000 continuous images. The vibration response of the blade can be obtained by normalizing displacement changes. Figures

Vibration displacement curves of point 1 under random excitation: (a)

Vibration displacement curves of point 10 under random excitation: (a)

Vibration displacement curves of point 1 under impact excitation: (a)

Vibration displacement curves of point 10 under impact excitation: (a)

3D space motion trajectories: (a) random excitation and (b) impact excitation.

The SSI-Data is performed to identify the modal parameters of the blade structure from photogrammetric response data. A Hankel matrix _{1} with 20 rows and 900 columns is constructed. The maximum model order is set to 100. Stabilization diagrams are drawn with frequency (abscissa coordinate) and the model order (ordinate coordinate). The results in _{2} with row number 30 and column number 850 and drew stabilization diagrams in the

Stabilization diagram based on SSI-Data:

Stabilization diagram (H2).

Stabilization diagram after eliminating spurious poles.

After eliminating spurious poles, we can further extract more accurate modal parameters by spectral clustering. The frequency is taken as abscissa coordinate, and the damping ratio is the ordinate coordinate; we have the clustering results as shown in Figure

Spectral clustering.

Stabilization diagram by the force hammer method.

The recognition results of blade’s modal frequencies.

Mode | Measurement method | ||
---|---|---|---|

Frequency (Hz) | |||

Proposed method | Impact test | Relative error (%) | |

First order | 4.42 | 4.28 | 3.2 |

Second order | 11.4 | 11.76 | −3.1 |

Third order | 28.23 | 29.01 | −2.7 |

Traditional contact measurement has many demerits for large-scale structures. A vibration detection method based on photogrammetry and modal parameters identification with improved SSI-Data is presented in this paper. The images of marked object points are continuously taken with binocular vision system and processed. Point tracking and matching are carried out to obtain the vibration response of marked points. The Hankel matrix is constructed with different dimensions for many times to produce different results of modal parameters. Similarity of these modal parameters is computed and clustered to form several stabilized groups. Experiments of a wind turbine blade are performed. The vibration of the blade tip is detected, and the modal parameters are identified with the presented algorithm. The modal frequencies are quite consistent with results of hammer pulse impact testing. It illustrates that photogrammetric vibration measurement and the new SSI-Data method are simple, efficient, and feasible for analyzing the dynamic characteristics of a large-scale irregular structure in applications.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was funded by the National Natural Science Foundation of China (nos. 51605157 and 61572185) and Hunan Provincial Innovation Foundation for Postgraduate (no. CX2016B546).