Bolted connections have been widely applied in engineering structures, loosening will happen when bolted connections are subjected to continuous cyclic load, and a significant rotation between the nut and the bolt can be observed. Combining deep learning with machine vision, a bolt loosening detection method based on the fifth version of You Only Look Once (YOLOv5) is proposed, and the rotation of the nut is identified to detect the bolt loosening. Two different circular markers are added to the bolt and the nut separately, and then YOLOv5 is used to identify the circular markers, and the rotation angle of the nut against the bolt is calculated according to the center coordinate of each predicted box. A bolted connection structure is adopted to illustrate the effectiveness of the method. First, 200 images containing bolts and circular markers are collected to make the dataset, which is divided into a training set, verification set and test set. Second, YOLOv5 is used to train the model; the precision rate and recall rate are respectively 99.8% and 100%. Finally, the robustness of the proposed method in different shooting environments is verified by changing the shooting distance, shooting angle and light condition. When using this method to detect the bolt loosening angle, the minimum identifiable angle is 1°, and the maximum detection error is 5.91% when the camera is tilted 45°. The experimental results show that the proposed method can detect the loosening angle of the bolted connection with high accuracy; especially, the tiny angle of bolt loosening can be identified. Even under some difficult shooting conditions, the method still works. The early stage of bolt loosening can be detected by measuring the rotation angle of the nut against the bolt.

We consider semigroup algorithmic problems in the Special Affine group SA(2, Z) = Z 2 ⋊SL(2, Z), which is the group of affine transformations of the lattice Z 2 that preserve orientation. Our paper focuses on two decision problems introduced by Choffrut and Karhumäki (2005): the Identity Problem (does a semigroup contain a neutral element?) and the Group Problem (is a semigroup a group?) for finitely generated sub-semigroups of SA(2, Z). We show that both problems are decidable and NP-complete. Since SL(2, Z) ≤ SA(2, Z) ≤ SL(3, Z), our result extends that of Bell, Hirvensalo and Potapov (SODA 2017) on the NP-completeness of both problems in SL(2, Z), and contributes a first step towards the open problems in SL(3, Z).

We show that the Identity Problem is decidable for finitely generated sub-semigroups of the group UT(4, Z) of 4 × 4 unitriangular integer matrices. As a byproduct of our proof, we have also shown the decidability of several subset reachability problems in UT(4, Z).

Let G be a finite set of matrices in a unipotent matrix group G over Q, where G has nilpotency class at most ten. We exhibit a polynomial time algorithm that computes the subset of G which generates the group of units of the semigroup G generated by G. In particular, this result shows that the Identity Problem and the Group Problem are decidable in polynomial time for finitely generated subsemigroups of the groups UT(11, Q) n . Another important implication of our result is the decidability of the Identity Problem and the Group Problem within finitely generated nilpotent groups of class at most ten. Our main idea is to analyze the logarithm of the matrices appearing in G . This allows us to employ Lie algebra methods to study this semigroup. In particular, we prove several new properties of the Baker-Campbell-Hausdorff formula, which help us characterize the convex cone spanned by the elements in log G .Furthermore, we formulate a sufficient condition in order for our results to generalize to unipotent matrix groups of class d > 10. For every such d, we exhibit an effective procedure that verifies this sufficient condition in case it is true.

Signal processing is important in the balancing of the motor armature, where the balancing accuracy depends on the extraction of the signal amplitude and phase from the raw vibration signal. In this study, a motor armature dynamic balancing method based on the long short-term memory network (LSTM) and zero-phase filter (ZPF) is proposed. This method mainly focuses on the extraction accuracy of amplitude and phase from unbalanced signals of the motor armature. The ZPF is used to accurately extract the phase, while the LSTM network is trained to extract the amplitude. The proposed method combines the advantages of both methods, whereby the problems of phase shift and amplitude loss when used alone are solved, and the motor armature unbalance signal is accurately obtained. The unbalanced mass and phase are calculated using the influence coefficient method. The effectiveness of the proposed method is proven using the simulated motor armature vibration signal, and an experimental investigation is undertaken to verify the dynamic balancing method. Two amplitude evaluation metrics and three phase evaluation metrics are proposed to judge the extraction accuracy of the amplitude and phase, whereas amplitude and frequency spectrum analysis are used to judge the dynamic balancing results. The results illustrate that the proposed method has higher dynamic balancing accuracy. Moreover, it has better extraction accuracy for the amplitude and phase of unbalanced signals compared with other methods, and it has good anti-noise performance. The determination coefficient of the amplitude is 0.9999, and the average absolute error of the phase is 2.4°. The proposed method considers both fidelity and denoising, which ensuring the accuracy of armature dynamic balancing.