Multi-Dimensional Uniform Initialization Gaussian Mixture Model for Spar Crack Quantification under Uncertainty

Mechanic-Electric-Thermal Directly Coupling Simulation Method of Lamb Wave under Temperature Effect

Lamb Wave (LW)-based structural health monitoring method is promising, but its main obstacle is damage assessment in varying environments. LW simulation based on piezoelectric transducers (referred to as PZTs) is an efficient and low-cost method. This paper proposes a multiphysics simulation method of LW propagation with the PZTs under temperature effect. The effect of temperature on LW propagation is considered from two aspects. On the one hand, temperature affects the material parameters of the structure, the adhesive layers and the PZTs. On the other hand, it is considered that the thermal stress caused by the inconsistency of thermal expansion coefficients among the structure, the adhesive layers, and the PZTs affect the piezoelectric constant of the PZTs. Based on the COMSOL Multiphysics, the mechanic-electric-thermal directly coupling simulation model under temperature effect is established. The simulation model consists of two steps. In the first step, the thermal-mechanic coupling is carried out to calculate the thermal stress, and the thermal stress effect is introduced into the piezoelectric constant model. In the second step, mechanic-electric coupling is carried out to simulate LW propagation, which considers the piezoelectric effect of the PZTs for the LW excitation and reception. The simulation results at -20 °C to 60 °C are obtained and compared to the experiment. The results show that the A₀ and S₀ mode of simulation signals match well with the experimental measurements. Additionally, the effect of temperature on LW propagation is consistent between simulation and experiment; that is, the amplitude increases, and the phase velocity decreases with the increment of temperature.

A New Clustering Method Based on the Inversion Formula

Data clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This paper presented a new density clustering method based on the modified inversion formula density estimation. This new method should allow one to improve the performance and robustness of the k-means, Gaussian mixture model, and other methods. The primary process of the proposed clustering algorithm consists of three main steps. Firstly, we initialized parameters and generated a T matrix. Secondly, we estimated the densities of each point and cluster. Third, we updated mean, sigma, and phi matrices. The new method based on the inversion formula works quite well with different datasets compared with K-means, Gaussian Mixture Model, and Bayesian Gaussian Mixture model. On the other hand, new methods have limitations because this one method in the current state cannot work with higher-dimensional data (d > 15). This will be solved in the future versions of the model, detailed further in future work. Additionally, based on the results, we can see that the MIDEv2 method works the best with generated data with outliers in all datasets (0.5%, 1%, 2%, 4% outliers). The interesting point is that a new method based on the inversion formula can cluster the data even if data do not have outliers; one of the most popular, for example, is the Iris dataset.