In multi-label learning, the subjectivity and instability of manual labeling often result in the absence of partial class labels and an incomplete label space. Missing labels are likely to be misleading in the training of supervised learning algorithms. The use of label correlation can alleviate the negative effect of missing labels on the algorithm classification performance to a certain extent. However, missing labels can lead to inaccurate estimations of label correlations. To address this problem, a method called multi-label learning with incomplete labels using an augmented label correlation matrix (ML-ALC) was proposed. First, a low-dimensional manifold of the data is constructed using Laplace mapping, and the original label correlation matrix is calculated using the label vectors. Subsequently, a correction matrix is constructed to augment the original label correlation matrix, and the original feature space and label space are mapped to the low-dimensional manifold through a regression coefficient matrix and augmented label correlation matrix, respectively. Finally, the optimized regression coefficient matrix and augmented label correlation matrix are obtained through iterative learning and applied to multi-label classification. The experimental results demonstrate that the proposed algorithm performs better than other state-of-the-art methods in multi-label learning with incomplete labels.

A method based on an improved particle swarm optimization algorithm was proposed to address the non-uniqueness problem of the inverse kinematics of a gravity compensation redundant manipulator and to obtain the optimal inverse kinematics solution for the manipulator with minimum displacement of the counterweight mass. First, the relationship between the displacement of the counterweight mass, joint angles, and servo compensation torque was analyzed using forward kinematics. Based on this, an inverse kinematics equation was constructed with the minimum displacement of the counterweight mass as the optimization objective and the position error accuracy as the constraint condition. An improved particle swarm optimization algorithm was used for the solution. The experimental results show that the optimal inverse kinematics solution for the manipulator with the minimum displacement of the counterweight mass as optimization objective was obtained, and that the non-uniqueness problem of the inverse kinematics was solved. This result is significant for follow-up experiments on the gravity-compensated redundant manipulator.

With increasing market competition and diversified customer demands, enterprises need to adopt flexible production methods to improve assembly efficiency and reduce production costs. Consequently, mixed-model assembly lines emerged in response to these challenges. Assembly line balancing and part feeding strategy are two critical decisions for ensuring an efficient assembly system. However, previous researches generally considered these problems separately, leading to an increase in total costs. Therefore, a mixed-integer programming (MIP) model is proposed for the joint optimization of assembly line balancing and part feeding strategy. The goal is to minimize the total costs of the assembly system, including assembly line costs, supermarket costs, and transportation costs. The model is validated through numerical examples and compared with the hierarchical model, confirming the necessity of the joint optimization approach. Sensitivity analysis shows that total costs decrease with increases in line-side space and kitting box size. However, constrained by factors such as cycle time, task allocation and part feeding strategy decisions will eventually stabilize.

In view of the fatigue damage to the fatigue detail I of the steel crane girder with abrupt right-angled change, an economic, effective, and feasible round steel tube reinforcement method was proposed. Specifically, a round steel tube was welded at the variable section of the crane girder, and a welding connection with the insert plate and the end sealing plate was performed. In order to evaluate the fatigue performance of the reinforced steel crane girder, a three-dimensional crack growth simulation was conducted based on linear elastic fracture mechanics. The results showed that this method could improve the local stress state of the steel crane girder with abrupt right-angled change. Compared with that before reinforcement, the stress amplitude at the fatigue detail I had decreased by nearly 40%, and the fatigue life of the steel crane girder had increased by 2 255 000 times. Through parameter analysis, the influence laws of different outer diameters and wall thicknesses of the round steel tube on the reinforcement effects and economic benefits were further explored, providing a reference basis for the application of crane girder fatigue reinforcement projects.

A finite element model was established to examine the ultimate state of reinforced concrete beams in nuclear power plants under accidental thermal loads. The FE model was validated by comparing the analysis results with those of published tests. Then, the validated finite element model was used to investigate the critical condition, ultimate capacity, and failure mode of the reinforced concrete beams under accidental thermal loads combined with other mechanical loads. The influence of the geometry constraint was considered, and the effects of the axial force, reinforcement ratio, and temperature on the load effect values were examined. The obtained cross-sectional thermal  bending moments were compared with the ACI Code values. The results showed that the thermal moment increased with an increase in the reinforcement ratio and temperature, and the ACI Code values appeared to overestimate the thermal bending moment, particularly in the case of high temperatures. As temperature increased, the ACI Code values became more conservative. Therefore, a formula was proposed to modify the flexural capacity calculated using the ACI Code. The results based on the formula were in good agreement with the finite element results under various operating conditions.

A new type of air-duct-embedded floor is presented in this study. The shear failure modes and mechanical properties of a cast-in-place air-duct embedded floor with longitudinal and transverse holes were studied using static tests. Based on the failure mechanism of the floor slab, a shear-bearing capacity calculation method for this floor type was proposed. The results show that the shear performance of a cast-in-place floor with embedded air ducts is better, that the shear capacity of a floor with an along-hole is greater than that of a floor with a cross-hole, and that the structure of a floor with an along-hole exhibits a good linear elastic performance before reaching peak load. In addition, this type of structure can be used in heat, ventilating and air conditioning (HVAC) ground-source heat pump air-conditioning systems to achieve the overall effects of green environmental protection and resource savings.

Ground vibrations caused by overloaded vehicles are influenced by factors such as vehicle weight, speed, road surface roughness, and soil parameters, making their attenuation patterns complex and difficult to accurately predict. This study characterizes and predicts the relationships between vehicle weight, speed, road surface roughness, soil parameters, and vibration attenuation performance. A prediction model for vibration response and attenuation at different sites under traffic loads is developed using a sparrow search algorithm (SSA)-optimized back propagation (BP) neural network. Additionally, a game-theory-based Shapley additive explanation (SHAP) algorithm is used for the model inter-pretability analysis. The results show that the model accurately simulates ground vibration propagation due to overloaded vehicles with high consistency in time- and frequency-domain characteristics when compared to field test data. Although the BP model exhibits prediction errors exceeding 10% for high-dispersity data, the SSA-BP model maintains high prediction accuracy across various datasets. In silty soil environments, the vehicle speed exhibits the strongest correlation with the vibration acceleration in the surrounding environment, whereas in clay and gravel environments, the distance from the vibration source exhibits the strongest correlation. The SHAP value analysis indicates that with the decrease in shear wave velocity, the effect of driving speed initially decreases and then increases, whereas the effects of vehicle weight and road surface grade gradually increase.

Removing constraints of internal supports of continuous cracked beam and instead of them with unknown reaction forces, the continuous cracked beam was simplified as a single span with unknown reaction forces. Based on the linear torsional spring model of transverse crack in beam, the general analytical solution of continuous Euler-Bernoulli beam with arbitrary number of open cracks on Winkler foundation was presented by Laplace transform and its inverse transformation. On the basis of verifying the correctness of the analytical solution using Abaqus finite element software, the influences of the foundation reaction coefficient, crack depth and location as well as beam length-height ratio on the bending deformation of continuous cracked beam were analyzed numerically. It is revealed that the deflection of the continuous cracked beam on Winkler foundation decreases with the foundation reaction coefficient increase. And the deflection cusp and rotation angle jump of beam at the crack location become more remarkable with increase of the crack depth; The influences of location, depth and numbers of the crack on the bending of cracked beam on Winkler foundation are remarkable. Furthermore, when the foundation reaction coefficient is larger, the influence of the crack on bending deformation of continuous beam on Winkler foundation diminishes gradually. These conclusions can provide certain guiding significance for structure design and structural health detection and monitoring.

We studied the global existence of classical solutions of two-dimensional axisymmetric Euler equations for dusty gas. We derived a group of characteristic decompositions for a two-dimensional axisymmetric Euler system. Using these characteristic decompositions, we determined a sufficient condition for the initial data to ensure the global existence of classical solutions to the Cauchy problem.

We construct the K₀-group of C^* algebra C^*(G) of finite group G. By investigating the projections of C^*(G) and the characters table of group G, we compute K₀(C^*(G)) explicitly.

Boundary value problem for a class of elliptic differential equations with a segment of turning points is considered. Firstly, using the method of multiple scales the formal asymptotic solution with turning points is constructed. And then, the uniform validity for the asymptotic expansion of the solution is proved by using the comparison theorem.

With respect to integrable partial differential equations, gauge transformations of Lax pairs are critical tools that can be used to extend integrable equations. We investigate gauge transformations for discrete integrable equations. By applying twice gauge transformations to the Lax pair of the discrete Korteweg—de Vries (KdV) equation, we obtain discrete modified KdV and discrete modified KdV-Ⅱ equations. Then, by introducing the potential variables, we obtain potential forms of those two equations, which are proven to satisfy the three-dimensional consistency property.

Load balancing is an important factor to improve the performance of large-scale parallel computing. A static load balancing method of multi-layer grid with one-dimensional partition is proposed for the lattice Boltzmann method. This hybrid method includes the optimization of computing domain allocation based on time load and the optimization of communication hiding. Theoretical analysis and experimental results show that this method can improve the load balance problem of parallel calculation of lattice Boltzmann method, and can be applied to large-scale accurate calculation of aircraft aerodynamic noise flow field and sound field.

Taking the 1-D nonlinear Maxwell's equation as a model, the multidomain Legendre tau method is studied for the cases of weak discontinuity and discontinuity at the interface of nonhomogeneous media. The leapfrog-Crank-Nicolson scheme is used for time discretization, which is a three-level explicit-implicit method of good stability and easy implementation. The stability of the scheme is proved, and the L²-error estimate of optimal order is obtained. Numerical examples show the effectiveness of the proposed multidomain Legendre tau method for such nonlinear discontinuous problems.