A class of uniformly bounded simple Z\mathbb{Z}-graded Lie conformal algebras

In this paper, we classify the following simple $\mathbb{Z}$-graded Lie conformal algebras $\mathcal{L}=\bigoplus_{i\in \mathbb{Z}}\mathcal{L}_i$ such that (1)$rank\mathcal{L}_i\leq 1$, (2)$\mathcal{L}_0$ is the Virasoro Lie conformal algebra

Invariant Teacher and Equivariant Student for Unsupervised 3D Human Pose Estimation

We propose a novel method based on teacher-student learning framework for 3D human pose estimation without any 3D annotation or side information. To solve this unsupervised-learning problem, the teacher network adopts pose-dictionary-based modeling for regularization to estimate a physically plausible 3D pose. To handle the decomposition ambiguity in the teacher network, we propose a cycle-consistent architecture promoting a 3D rotation-invariant property to train the teacher network. To further improve the estimation accuracy, the student network adopts a novel graph convolution network for flexibility to directly estimate the 3D coordinates. Another cycle-consistent architecture promoting 3D rotation-equivariant property is adopted to exploit geometry consistency, together with knowledge distillation from the teacher network to improve the pose estimation performance. We conduct extensive experiments on Human3.6M and MPI-INF-3DHP. Our method reduces the 3D joint prediction error by 11.4% compared to state-of-the-art unsupervised methods and also outperforms many weakly-supervised methods that use side information on Human3.6M. Code will be available at https://github.com/sjtuxcx/ITES.Comment: Accepted in AAAI 202

Performance assessment of natural frequencies in characterizing cracks in beams in noisy conditions

Numerical cases of the use of natural frequencies to identify crack location and crack depth in beams under noise-free conditions have been widely reported. However, the capability of natural frequencies to identify cracks in noisy conditions has not yet been systematically addressed. Unlike previous work stressing the merits of natural frequencies in depicting cracks, this study reports the performance assessment of natural frequencies in characterizing cracks in noisy conditions. In the performance assessment, a cracked cantilever Timoshenko beam, with the crack flexibility modeled by fracture mechanics principles, is considered. The results demonstrate quantitatively and exhaustively that natural frequencies, as global dynamic properties of a structure, are somewhat insensitive to local slight damage. The outcome of this study provides a guideline for rational use of natural frequencies to identify cracks in actual beam-type structures

Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures

Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV) providing a chance to reliably acquire higher-order (around tenth-order) mode shapes, an improved fractal dimension method that is capable of treating higher-order mode shapes for damage detection is of important significance. This study proposes a sophisticated fractal dimension method with the aid of a specially designed affine transformation that is able to obviate natural inflexions of a higher-order mode shape while preserving its substantial damage information. The affine transformed mode shape facilitates the fractal dimension analysis to yield an effective damage feature: fractal dimension trajectory, in which an abruptly risking peak clearly characterizes the location and severity of the damage. This new fractal dimension method is demonstrated on multiple cracks identification in numerically simulated damage scenarios. The effectiveness of the method is experimentally validated by using a SLV to acquire higher-order mode shapes of a cracked cantilever beam

Performance assessment of natural frequencies in characterizing cracks in beams in noisy conditions

Numerical cases of the use of natural frequencies to identify crack location and crack depth in beams under noise-free conditions have been widely reported. However, the capability of natural frequencies to identify cracks in noisy conditions has not yet been systematically addressed. Unlike previous work stressing the merits of natural frequencies in depicting cracks, this study reports the performance assessment of natural frequencies in characterizing cracks in noisy conditions. In the performance assessment, a cracked cantilever Timoshenko beam, with the crack flexibility modeled by fracture mechanics principles, is considered. The results demonstrate quantitatively and exhaustively that natural frequencies, as global dynamic properties of a structure, are somewhat insensitive to local slight damage. The outcome of this study provides a guideline for rational use of natural frequencies to identify cracks in actual beam-type structures

Performance assessment of natural frequencies in characterizing cracks in beams in noisy conditions

Numerical cases of the use of natural frequencies to identify crack location and crack depth in beams under noise-free conditions have been widely reported. However, the capability of natural frequencies to identify cracks in noisy conditions has not yet been systematically addressed. Unlike previous work stressing the merits of natural frequencies in depicting cracks, this study reports the performance assessment of natural frequencies in characterizing cracks in noisy conditions. In the performance assessment, a cracked cantilever Timoshenko beam, with the crack flexibility modeled by fracture mechanics principles, is considered. The results demonstrate quantitatively and exhaustively that natural frequencies, as global dynamic properties of a structure, are somewhat insensitive to local slight damage. The outcome of this study provides a guideline for rational use of natural frequencies to identify cracks in actual beam-type structures

Identification of Damage on Sluice Hoist Beams Using Local Mode Evoked by Swept Frequency Excitation

As a global vibration characteristic, natural frequency often suffers from insufficient sensitivity to structural damage, which is associated with local variations of structural material or geometric properties. Such a drawback is particularly significant when dealing with the large scale and complexity of sluice structural systems. To this end, a damage detection method in sluice hoist beams is proposed that relies on the utilization of the local primary frequency (LPF), which is obtained based on the swept frequency excitation (SFE) technique and local resonance response band (LRRB) selection. Using this method, the local mode of the target sluice hoist beam can be effectively excited, while the vibrations of other components in the system are suppressed. As a result, the damage will cause a significant shift in the LPF of the sluice hoist beam at the local mode. A damage index was constructed to quantitatively reflect the damage degree of the sluice hoist beam. The accuracy and reliability of the proposed method were verified on a three-dimensional finite element model of a sluice system, with the noise resistance increased from 0.05 to 0.2 based on the hammer impact method. The proposed method exhibits promising potential for damage detection in complex structural systems