The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R₀ = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.

The accurate forecasting of metal prices is of great importance to industrial producers as the supply of metal raw materials is a very important part of industrial production. The futures market is subject to many factors, and metal prices are highly volatile. In the past, most of the relevant research has focused only on deterministic point forecasting, with less research performed on interval uncertainty forecasting. Therefore, this paper proposes a novel forecasting model that combines point forecasting and interval forecasting. First, a novel hybrid price point forecasting model was established using Variational Modal Decomposition (VMD) and a Long Short-Term Memory Neural Network (LSTM) based on Sparrow Search Algorithm (SSA) optimization. Then, five distribution functions based on the optimization algorithm were used to fit the time series data patterns and analyze the metal price characteristics, Finally, based on the optimal distribution function and point forecasting results, the forecasting range and confidence level were set to determine the interval forecasting model. The interval forecasting model was validated by inputting the price data of copper and aluminum into the model and obtaining the interval forecasting results. The validation results show that the proposed hybrid forecasting model not only outperforms other comparative models in terms of forecasting accuracy, but also has a better performance in forecasting sharp fluctuations and data peaks, which can provide a more valuable reference for producers and investors.

The current global resource shortage and environmental pollution are becoming increasingly serious, and the development of the new energy vehicle industry has become one of the important issues of the times. In this paper, a nickel–cobalt lithium manganate (NCM) battery for a pure electric vehicle is taken as the research object, a heat dissipation design simulation is carried out using COMSOL software, and a charging heat generation model of the battery pack is established. Combined with the related research on the thermal management technology of the lithium-ion battery, five liquid-cooled temperature control models are designed for thermal management, and their temperature control simulation and effect analysis are carried out. Finally, the performance evaluation system of the thermal management scheme of the lithium-ion battery pack is established based on the analytic network process (ANP) and system dynamics (SD), and the performance of the above five thermal management design models is comprehensively scored and analyzed. The results show that liquid-cooled Models 1 (86.7075) and 5 (89.1055) have the highest overall scores, meeting both the temperature control requirements and the overall thermal management performance, and it is recommended to apply the working condition settings for which they are evaluated as Level I.

Mine extraction planning has a far-reaching impact on the production management and overall economic efficiency of the mining enterprise. The traditional method of preparing underground mine production planning is complicated and tedious, and reaching the optimum calculation results is difficult. Firstly, the theory and method of multi-objective optimization are used to establish a multi-objective planning model with the objective of the best economic efficiency, grade, and ore quantity, taking into account the constraints of ore grade fluctuation, ore output from the mine, production capacity of mining enterprises, and mineral resources utilization. Second, an improved particle swarm algorithm is applied to solve the model, a nonlinear dynamic decreasing weight strategy is proposed for the inertia weights, the variation probability of each generation of particles is dynamically adjusted by the aggregation degree, and this variation probability is used to perform a mixed Gaussian and Cauchy mutation for the global optimal position and an adaptive wavelet variation for the worst individual optimal position. This improved strategy can greatly increase the diversity of the population, improve the global convergence speed of the algorithm, and avoid the premature convergence of the solution. Finally, taking a large polymetallic underground mine in China as a case, the example calculation proves that the algorithm solution result is 10.98% higher than the mine plan index in terms of ore volume and 41.88% higher in terms of economic efficiency, the algorithm solution speed is 29.25% higher, and the model and optimization algorithm meet the requirements of a mining industry extraction production plan, which can effectively optimize the mine’s extraction plan and provide a basis for mine operation decisions.

In this paper, a multi-point geostatistical (MPS) method based on variational function partition simulation is proposed to solve the key problem of MPS 3D modeling using 2D training images. The new method uses the FILTERSIM algorithm framework, and the variational function is used to construct simulation partitions and training image sequences, and only a small number of training images close to the unknown nodes are used in the partition simulation to participate in the MPS simulation. To enhance the reliability, a new covariance filter is also designed to capture the diverse features of the training patterns and allow the filter to downsize the training patterns from any direction; in addition, an information entropy method is used to reconstruct the whole 3D space by selecting the global optimal solution from several locally similar training patterns. The stability and applicability of the new method in complex geological modeling are demonstrated by analyzing the parameter sensitivity and algorithm performance. A geological model of a uranium deposit is simulated to test the pumping of five reserved drill holes, and the results show that the accuracy of the simulation results of the new method is improved by 11.36% compared with the traditional MPS method.