Tool condition monitoring (TCM) is of great importance for improving the manufacturing efficiency and surface quality of workpieces. Data-driven machine learning methods are widely used in TCM and have achieved many good results. However, in actual industrial scenes, labeled data are not available in time in the target domain that significantly affect the performance of data-driven methods. To overcome this problem, a new TCM method combining the Markov transition field (MTF) and the deep domain adaptation network (DDAN) is proposed. A few vibration signals collected in the TCM experiments were represented in 2D images through MTF to enrich the features of the raw signals. The transferred ResNet50 was used to extract deep features of these 2D images. DDAN was employed to extract deep domain-invariant features between the source and target domains, in which the maximum mean discrepancy (MMD) is applied to measure the distance between two different distributions. TCM experiments show that the proposed method significantly outperforms the other three benchmark methods and is more robust under varying working conditions.

Rolling bearings are crucial mechanical components in the mechanical industry. Timely intervention and diagnosis of system faults are essential for reducing economic losses and ensuring product productivity. To further enhance the exploration of unlabeled time-series data and conduct a more comprehensive analysis of rolling bearing fault information, this paper proposes a fault diagnosis technique for rolling bearings based on graph node-level fault information extracted from 1D vibration signals. In this technique, 10 categories of 1D vibration signals from rolling bearings are sampled using a sliding window approach. The sampled data is then subjected to wavelet packet decomposition (WPD), and the wavelet energy from the final layer of the four-level WPD decomposition in each frequency band is used as the node feature. The weights of edges between nodes are calculated using the Pearson correlation coefficient (PCC) to construct a node graph that describes the feature information of rolling bearings under different health conditions. Data augmentation of the node graph in the dataset is performed by randomly adding nodes and edges. The graph convolutional neural network (GCN) is employed to encode the augmented node graph representation, and deep graph contrastive learning (DGCL) is utilized for the pre-training and classification of the node graph. Experimental results demonstrate that this method outperforms contrastive learning-based fault diagnosis methods for rolling bearings and enables rapid fault diagnosis, thus ensuring the normal operation of mechanical systems. The proposed WPDPCC-DGCL method offers two advantages: (1) the flexibility of wavelet packet decomposition in handling non-smooth vibration signals and combining it with the powerful multi-scale feature encoding capability of GCN for richer characterization of fault information, and (2) the construction of graph node-level fault samples to effectively capture underlying fault information. The experimental results demonstrate the superiority of this method in rolling bearing fault diagnosis over contrastive learning-based approaches, enabling fast and accurate fault diagnoses for rolling bearings and ensuring the normal operation of mechanical systems.

Packing soft rectangular objects in an optimized convex container is considered. Each soft rectangle can be freely translated and rotated, has a fixed area, and its dimensions can vary in certain limits. The convex container may have prohibited zones where allocation of the objects is not allowed. The soft rectangles must be arranged completely inside the container; mutual intersection and overlapping with prohibited zones is not allowed. The objective is to minimize a certain metric characteristic of the container. The corresponding nonlinear mathematical problem is formulated using the phi-function technique to present non-overlapping and containment conditions. A model-based heuristic is proposed to find reasonable solutions to the problem. Numerical results are provided for triangular, circular, and scaled polygonal containers to validate the model and demonstrate the proposed approach’s efficiency.

Recent advances in artificial intelligence (AI) technology have led to increasing interest in the development of AI-based tool wear condition monitoring methods, heavily relying on large training samples. However, the high cost of tool wear experiment and the uncertainty of tool wear change in the machining process lead to the problems of sample missing and insufficiency in the model training stage, which seriously affects the identification accuracy of many AI models. In this paper, a novel identification method based on finite-element modeling (FEM) and the synthetic minority oversampling technique (SMOTE) is proposed to overcome the problem of sample missing and sample insufficiency. Firstly, a few tool wear monitoring experiments are carried out to obtain experimental samples with low cost. Then, a FEM model based on the Johnson–Cook constitutive model was established and verified according to the experimental samples. Based on the verified FEM model, the simulated missing sample in the experiments can be supplemented to compose a complete training set. Finally, the SMOTE is employed to expand the sample size to construct a perfect training set to train the SVM classification model. End milling tool wear monitoring experiments demonstrate that the proposed FEM-SMOTE method can obtain 98.7% identification accuracy, which is 30% higher than that based on experimental samples. The proposed method provides an effective approach for tool wear condition monitoring with low experimental cost.