Liangliang Cheng

Yanxin Si, Bayu Jayawardhana, J. Nathan Kutz et al.

Experimental Modal Analysis (EMA) has been widely used to identify structural dynamic properties, including natural frequencies, damping ratios, and mode shapes, for structural integrity assessment. The Poly-reference Least Squares Complex Frequency (pLSCF) method is one of the most widely adopted approaches for EMA because of its strong ability to separate closely spaced modes and its robustness to measurement noise. However, pLSCF-based EMA is generally limited to low-dimensional cases with a small number of measurement points, as its computational cost increases rapidly for high-dimensional or continuous structural measurements, particularly with increasing model order. To overcome this limitation, this paper develops a high-dimensional EMA framework based on Dynamic Mode Decomposition with control (DMDc), a powerful data-driven technique originally developed in fluid dynamics, for modal identification under high-dimensional measurement scenarios. Specifically, the relationship between pLSCF and time-delay DMDc is clarified through the discrete state-space representation of the auto-regressive with exogenous inputs (ARX) model for linear systems. By showing that both methods describe the same physical dynamics of the structure, this study provides a physics-based rationale for applying time-delay DMDc to EMA. The capability and advantages of time-delay DMDc for modal parameter identification in both low- and high-dimensional measurements are validated through numerical simulations of a 6-DOF system and experiments on a cantilever beam using a digital camera. The results demonstrate that time-delay DMDc enables robust and reliable modal parameter identification, effectively addressing high-dimensional EMA problems that are difficult for conventional pLSCF and highlighting its potential for real-world structural dynamics applications.

Yunpeng Zhu, Liangliang Cheng, Anping Jing et al.

We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a low-rank subspace spanning multiple experiments in parameter space. The proposed inverse design dynamic mode composition (ID-DMD) algorithm leverages the computed low-dimensional subspace to enable fast digital design and optimization on laptop-level computing, including the potential to prescribe the dynamics themselves. Moreover, the method is robust to noise, physically interpretable, and can provide uncertainty quantification metrics. The architecture can also efficiently scale to large-scale design problems using randomized algorithms in the ID-DMD. The simplicity of the method and its implementation are highly attractive in practice, and the ID-DMD has been demonstrated to be an order of magnitude more accurate than competing methods while simultaneously being 3-5 orders faster on challenging engineering design problems ranging from structural vibrations to fluid dynamics. Due to its speed, robustness, interpretability, and ease-of-use, ID-DMD in comparison with other leading machine learning methods represents a significant advancement in data-driven methods for inverse design and optimization, promising a paradigm shift in how to approach inverse design in practice.

Vahid Yaghoubi, Liangliang Cheng, Wim Van Paepegem et al.

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.

Vahid Yaghoubi, Liangliang Cheng, Wim Van Paepegem et al.

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.

Vahid Yaghoubi, Liangliang Cheng, Wim Van Paepegem et al.

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.

Vahid Yaghoubi, Liangliang Cheng, Wim Van Paepegem et al.

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.