A Sequence-Based Damage Identification Method for Composite Rotors by Applying the Kullback-Leibler Divergence, a Two-Sample Kolmogorov-Smirnov Test and a Statistical Hidden Markov Model

On the Symmetry Importance in a Relative Entropy Analysis for Some Engineering Problems

This paper aims at certain theoretical studies and additional computational analysis on symmetry and its lack in Kullback-Leibler and Jeffreys probabilistic divergences related to some engineering applications. As it is known, the Kullback-Leibler distance in between two different uncertainty sources exhibits a lack of symmetry, while the Jeffreys model represents its symmetrization. The basic probabilistic computational implementation has been delivered in the computer algebra system MAPLE 2019®, whereas engineering illustrations have been prepared with the use of the Finite Element Method systems Autodesk ROBOT® & ABAQUS®. Determination of the first two probabilistic moments fundamental in the calculation of both relative entropies has been made (i) analytically, using a semi-analytical approach (based upon the series of the FEM experiments), and (ii) the iterative generalized stochastic perturbation technique, where some reference solutions have been delivered using (iii) Monte-Carlo simulation. Numerical analysis proves the fundamental role of computer algebra systems in probabilistic entropy determination and shows remarkable differences obtained with the two aforementioned relative entropy models, which, in some specific cases, may be neglected. As it is demonstrated in this work, a lack of symmetry in probabilistic divergence may have a decisive role in engineering reliability, where extreme and admissible responses cannot be simply replaced with each other in any case.

Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.

Structural Damage Identification of Composite Rotors Based on Fully Connected Neural Networks and Convolutional Neural Networks

Damage identification of composite structures is a major ongoing challenge for a secure operational life-cycle due to the complex, gradual damage behaviour of composite materials. Especially for composite rotors in aero-engines and wind-turbines, a cost-intensive maintenance service has to be performed in order to avoid critical failure. A major advantage of composite structures is that they are able to safely operate after damage initiation and under ongoing damage propagation. Therefore, a robust, efficient diagnostic damage identification method would allow monitoring the damage process with intervention occurring only when necessary. This study investigates the structural vibration response of composite rotors by applying machine learning methods and the ability to identify, localise and quantify the present damage. To this end, multiple fully connected neural networks and convolutional neural networks were trained on vibration response spectra from damaged composite rotors with barely visible damage, mostly matrix cracks and local delaminations using dimensionality reduction and data augmentation. A databank containing 720 simulated test cases with different damage states is used as a basis for the generation of multiple data sets. The trained models are tested using k-fold cross validation and they are evaluated based on the sensitivity, specificity and accuracy. Convolutional neural networks perform slightly better providing a performance accuracy of up to 99.3% for the damage localisation and quantification.

A Cross-Reconstruction Method for Step-Changed Runoff Series to Implement Frequency Analysis under Changing Environment

The stationarity of observed hydrological series has been broken or destroyed in many areas worldwide due to changing environments, causing hydrologic designs under stationarity assumption to be questioned and placing designed projects under threat. This paper proposed a data expansion approach-namely, the cross-reconstruction (CR) method-for frequency analysis for a step-changed runoff series combined with the empirical mode decomposition (EMD) method. The purpose is to expand the small data on each step to meet the requirements of data capacity for frequency analysis and to provide more reliable statistics within a stepped runoff series. Taking runoff records at three gauges in western China as examples, the results showed that the cross-reconstruction method has the advantage of data expansion of the small sample runoff data, and the expanded runoff data at steps can meet the data capacity requirements for frequency analysis. In addition, the comparison of the expanded and measured data at steps indicated that the expanded data can demonstrate the statistics closer to the potential data population, rather than just reflecting the measured data. Therefore, it is considered that the CR method ought to be available in frequency analysis for step-changed records, can be used as a tool to construct the hydrological probability distribution under different levels of changing environments (at different steps) through data expansion, and can further assist policy-making in water resources management in the future.