This article proposes a new method for bearing fault diagnosis based on sparse representation classification to address the challenges of fault identification under complex working conditions with different degrees of damage. The core of this method lies in directly using the original vibration signal to construct an overcomplete dictionary without the need for signal denoising or manual feature extraction in advance, thus avoiding the information loss and subjective bias introduced by denoising and feature engineering in traditional methods. Firstly, all training samples are used as a dictionary to sequentially solve for sparse coefficients for each test sample. Secondly, the corresponding parts of each category in the sparse coefficients are filtered out. Then, the category error is calculated based on the sparse coefficients corresponding to each category. Finally, the fault classification of bearings is carried out by comparing the category errors. The experimental results show that this method can maintain high diagnostic accuracy and robustness in complex scenarios with various working conditions and damage levels, verifying its effectiveness and universality for bearing fault diagnosis.

This paper studies a vehicle routing problem with simultaneous pickup and delivery (VRPSPD), which has an important application in logistics and other areas. The problem is that the depot provides both forward supply service and reverse recovery service to customers, and determines the lowest-cost vehicle distribution routes that satisfy the needs of all customers on the basis of considering constraints. To solve this problem, we develop an improved ant colony optimization algorithm based on candidate strategy and grid search (ACO-CS). The candidate strategy of ACO-CS reduces the running cost and speeds up the convergence rate by limiting and reducing the number of unvisited nodes. At the same time, we propose to use the grid search method to tune the parameters to enhance the algorithm’s optimization capability and improve its performance. Three benchmark test problems are selected to verify the effectiveness of the proposed algorithm for solving different types and sizes of instances. The computational results show that the proposed algorithm is competitive in solving the Dethloff (2001) and Montane & Galveo (2006) test problems, and its solution quality, calculation time and algorithm stability are better than the variant algorithms in the literature. Finally, a practical case of logistics distribution is introduced to verify the reliability of the algorithm, and the results show that the ACO-CS can provide a more reasonable and economical solution.

The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding wave equation without damping term and mass term. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems $ 1.1-1.4 $ are new. Moreover, the changing trends of semilinear wave equations are illustrated through numerical simulation.

The main goal of this paper is to study blow‐up of solutions of a weakly coupled system for semilinear wave equations with damping terms and mass terms in the de Sitter spacetime. The exponential, polynomial, and logarithmic growth of time‐dependent factors in nonlinear terms are investigated by using iterative methods, respectively. Upper bound lifespan estimates of solutions to the problem are established. To the best of our knowledge, the results in Theorems 1.1–1.3 are new. In particular, the critical curve for exponents ( p , q ) in nonlinear terms in this problem is same as the critical curve for a weakly coupled system of semilinear wave equations with power nonlinearities. In addition, wave trends are expressed by numerical simulation.