“…Theoretically, the time recorded by the sensor when the blade does not vibrate can be calculated using equation (1), 40 where fr is the rotation frequency, αi is the installation angle of the BTT sensor, n denotes the number of turns, and θk represents the angle between the k th blade and the reflective mark on the shaft. Because of the vibration generated during operation, when the k th blade passes the i th sensor, the actual arrival time can be expressed as shown in equation (2), 40 where y represents the displacement of the blade, and r is the radius of rotation of the blade. Then, the displacement of the blade can be obtained using equation (3):Figure 1.Blade tip timing system.…”
Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities.
“…Theoretically, the time recorded by the sensor when the blade does not vibrate can be calculated using equation (1), 40 where fr is the rotation frequency, αi is the installation angle of the BTT sensor, n denotes the number of turns, and θk represents the angle between the k th blade and the reflective mark on the shaft. Because of the vibration generated during operation, when the k th blade passes the i th sensor, the actual arrival time can be expressed as shown in equation (2), 40 where y represents the displacement of the blade, and r is the radius of rotation of the blade. Then, the displacement of the blade can be obtained using equation (3):Figure 1.Blade tip timing system.…”
Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities.
“…If the artificial biology survives for a certain age, develop to maturity, and then they may breed the next generation. The next generation will inherit the good genes of parents, strategy and initial energy of parents, at same time in order to keep variety of biology, the certain mutation rate should be considered in procession of breeding 7 .…”
The trajectory planning optimization can improve the performance of robot, and therefore the artificial life system method is applied in arc trajectory planning of robot. Firstly, the mathematical model of arc trajectory planning of robot is analyzed. Secondly, the basic theory of artificial life system is studied, and the corresponding algorithm procedure is designed. Finally, the simulation analysis is carried out, and the optimal trajectory of robot is obtained, and results shown that the artificial life system optimization method can be applied in the trajectory planning of robot effectively.
“…Early synchronous vibration was analyzed using the single-parameter plot method [11], two-parameter plot method [12,13], and autoregressive method [14]. Subsequently, several methods have been developed for asynchronous vibration, such as '5 + 2' scheme [15], NUFT method [16], linear regression method [17], multichannel interpolation method [18,19] and compressed sensing method [20,21]. However, most methods only focus on the resonance frequencies and amplitudes of vibrations and fail in damping ratio identification, especially in asynchronous vibration analysis.…”
Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.
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