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Non-destructive testing on metallic turbine blades is a challenging task due to their complex geometry. Vibrational test-ing such as Process Compensated Resonance Testing (PCRT) has shown an efficient approach, which first measures the vibrational response of the turbine blades, and then employs a classifier to determine if the quality of the turbine blades are good or bad. Our previous work mainly concentrated on the development of Mahalanobis distance-based classifiers which are fed by the measured vibrational features (such as resonant frequencies). In practice, however, measurement errors could lead to a biased trained classifier, potentially resulting in the wrong quality classifications of the turbine blade. In this study, we investigate the classification problem of turbine blades under measurement uncertainty. For this, the concept of Interval Mahalanobis Space is employed, leading to the Integrated Interval Mahalanobis Classification system (IIMCS) classifier which has high robustness against measurement uncertainty. The IIMCS employs Binary Particle Swarm Optimization (BPSO) to filter out those resonant frequencies which contrib-ute most to the information in the system. A Monte Carlo Simulation scheme is employed to analyze the sensitivity of the resonant frequencies to the measurement uncertainty. This yields an indicator of reliability, indicating the confidence level of the final classification results. The developed IIMCS methodology is applied to an experimental case study of equiaxed nickel alloy first-stage turbine blades, showing good and robust classification performance., Comment: END&CM2021

Nowadays, using vibration data in conjunction with pattern recognition methods is one of the most common fault detection strategies for structures. However, their performances depend on the features extracted from vibration data, the features selected to train the classifier, and the classifier used for pattern recognition. Deep learning facilitates the fault detection procedure by automating the feature extraction and selection, and classification procedure. Though, deep learning approaches have challenges in designing its structure and tuning its hyperparameters, which may result in a low generalization capability. Therefore, this study proposes an ensemble deep learning framework based on a convolutional neural network (CNN) and Dempster-Shafer theory (DST), called CNN-DST. In this framework, several CNNs with the proposed structure are first trained, and then, the outputs of the CNNs selected by the proposed technique are combined by using an improved DST-based method. To validate the proposed CNN-DST framework, it is applied to an experimental dataset created by the broadband vibrational responses of polycrystalline Nickel alloy first-stage turbine blades with different types and severities of damage. Through statistical analysis, it is shown that the proposed CNN-DST framework classifies the turbine blades with an average prediction accuracy of 97.19%. The proposed CNN-DST framework is benchmarked with other state-of-the-art classification methods, demonstrating its high performance. The robustness of the proposed CNN-DST framework with respect to measurement noise is investigated, showing its high noise-resistance. Further, bandwidth analysis reveals that most of the required information for detecting faulty samples is available in a small frequency range.

Vibration-based techniques are among the most common condition monitoring approaches. With the advancement of computers, these approaches have also been improved such that recently, these approaches in conjunction with deep learning methods attract attention among researchers. This is mostly due to the nature of the deep learning method that could facilitate the monitoring procedure by integrating the feature extraction, feature selection, and classification steps into one automated step. However, this can be achieved at the expense of challenges in designing the architecture of a deep learner, tuning its hyper-parameters. Moreover, it sometimes gives low generalization capability. As a remedy to these problems, this study proposes a framework based on ensemble deep learning methodology. The framework was initiated by creating a pool of Convolutional neural networks (CNN). To create diversity to the CNNs, they are fed by frequency responses which are passed through different functions. As the next step, proper CNNs are selected based on an information criterion to be used for fusion. The fusion is then carried out by improved Dempster-Shafer theory. The proposed framework is applied to real test data collected from Equiax Polycrystalline Nickel alloy first-stage turbine blades with complex geometry.

Achieving a high prediction rate is a crucial task in fault detection. Although various classification procedures are available, none of them can give high accuracy in all applications. Therefore, in this paper, a novel multi-classifier fusion approach is developed to boost the performance of the individual classifiers. This is acquired by using Dempster-Shafer theory (DST). However, in cases with conflicting evidences, the DST may give counter-intuitive results. In this regard, a preprocessing technique based on a new metric is devised in order to measure and mitigate the conflict between the evidences. To evaluate and validate the effectiveness of the proposed approach, the method is applied to 15 benchmarks datasets from UCI and KEEL. Further, it is applied for classifying polycrystalline Nickel alloy first-stage turbine blades based on their broadband vibrational response. Through statistical analysis with different noise levels, and by comparing with four state-of-the-art fusion techniques, it is shown that that the proposed method improves the classification accuracy and outperforms the individual classifiers., Comment: arXiv admin note: text overlap with arXiv:2007.08789

Vibration-based quality monitoring of manufactured components often employs pattern recognition methods. Albeit developing several classification methods, they usually provide high accuracy for specific types of datasets, but not for general cases. In this paper, this issue has been addressed by developing a novel ensemble classifier based on the Dempster-Shafer theory of evidence. To deal with conflicting evidences, three remedies are proposed prior to combination: (i) selection of proper classifiers by evaluating the relevancy between the predicted and target outputs, (ii) devising an optimization method to minimize the distance between the predicted and target outputs, (iii) utilizing five different weighting factors, including a new one, to enhance the fusion performance. The effectiveness of the proposed framework is validated by its application to 15 UCI and KEEL machine learning datasets. It is then applied to two vibration-based datasets to detect defected samples: one synthetic dataset generated from the finite element model of a dogbone cylinder, and one real experimental dataset generated by collecting broadband vibrational response of polycrystalline Nickel alloy first-stage turbine blades. The investigation is made through statistical analysis in presence of different levels of noise-to-signal ratio. Comparing the results with those of four state-of-the-art fusion techniques reveals the good performance of the proposed ensemble method.

The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods have been developed to automate this procedure. The common approach is to identify models with different orders and cluster similar modes together. However, most proposed methods based on this approach suffer from high-dimensional optimization problems in either the estimation or clustering step. To overcome this problem, this study presents an algorithm for autonomous modal parameter estimation in which the only required optimization is performed in a three-dimensional space. To this end, a subspace-based identification method is employed for the estimation and a non-iterative correlation-based method is used for the clustering. This clustering is at the heart of the paper. The keys to success are correlation metrics that are able to treat the problems of spatial eigenvector aliasing and nonunique eigenvectors of coalescent modes simultaneously. The algorithm commences by the identification of an excessively high-order model from frequency response function test data. The high number of modes of this model provide bases for two subspaces: one for likely physical modes and one for its complement dubbed the subspace of noise modes. By employing the bootstrap resampling technique, several subsets are generated from the same basic dataset and for each of them a model is identified to form a set of models. Then, by correlation analysis, highly correlated modes of these models which appear repeatedly are clustered together and the noise modes are collected in a so-called Trashbox cluster. Stray noise modes attracted to the mode clusters are trimmed away by correlation analysis. The final step is a fuzzy c-means clustering procedure.

In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel splitting approach. While Magnus expansion has been intensely studied and widely applied for solving explicitly time-dependent problems, it can also be extended to nonlinear problems. By the way it is delicate to extend, while an exponential character have to be computed. Alternative methods, like successive approximation methods, might be an attractive tool, which take into account the temporally in-homogeneous equation (method of Tanabe and Sobolevski). In this work, we consider nonlinear stability analysis with numerical experiments and compare standard integrators to our novel approaches., Comment: 22 pages