Mathematical Problems in Engineering

The fluctuation of microgrid power flow leads to serious voltage problems at the point of common coupling (PCC). The quantitative representation of the disturbance parameters of the voltage waveform at the PCC is necessary for evaluating and controlling the impact of distributed generation in the microgrid on the power system. An improved atomic decomposition (IAD) method is proposed to represent the disturbance parameters quantitatively and efficiently. Based on the disturbance characteristics of the PCC voltage, a coherent atom dictionary composed of four subdictionaries is constructed to improve the decomposition efficiency. To further improve the computational efficiency, an improved matching pursuits algorithm is proposed by alternating the search way to extract the disturbance components in the atomic decomposition. Meanwhile, simulation results show that the proposed IAD method has better antinoise and disturbance parameters quantization ability than wavelet transform.

China, situated in the circum-Pacific seismic belt, experiences frequent seismic activity and faces diverse geological conditions, making structural stability of paramount importance, especially under seismic conditions. The majority of current earthquake generation methods do not consider the nonstationary nature of earthquakes. This paper introduces a spectral representation-random function model for generating nonstationary earthquakes, effectively simulating stochastic seismic ground motion. Furthermore, traditional slope stability analysis methods are deterministic and incapable of providing probabilistic assessments of slope instability. Therefore, this paper proposes a unified framework for static and dynamic structural reliability analysis based on the direct probability integration method, quantifying the impact of stochastic seismic ground motion on the dynamic reliability of slope stability. Finally, the proposed methods are applied to an excavation slope in Nanjing, using sliding displacement and safety factors as evaluation criteria to study the reliability of the slope under the influence of stochastic seismic events.

Spin separation technology is a key technology for realizing the detection function at the end of the rotational trajectory. It is also a necessary condition for the fuse control system to adjust its control strategy according to actual combat needs. To explore a new type of proximity fuse detection method, this article first designs a detection separation mechanism for the end of the trajectory. An interior ballistic model of the separation mechanism was then established through closed bomb tests and equivalent interior ballistic equations, and the aerodynamic parameters of the front-stage separation body at the moment of separation were obtained based on computational fluid dynamics numerical simulation. Finally, a separation dynamics model of the separation mechanism was established to analyze the motion state after the separation action of the front-stage separation body. The results demonstrate the feasibility of the proposed separation mechanism. The discrepancy between the simulation and experiment of the velocity increment for the front-stage separation body is about 1.07%. The attack angle for the front-stage separation body is below 2°, and the period with a displacement between two stage bodies greater than 3 m is around 0.365 s. This research can provide new ideas and theoretical references for the design of a similar fuse detection separation mechanism.

The paired approach can improve the efficiency of closely spaced parallel runways. Calculating the probability and frequency of horizontal overlap is an indispensable step when evaluating the horizontal collision risk of the paired approach. As the generation of horizontal overlap probability is closely related to horizontal position error, we propose a calculation method of horizontal overlap probability based on position error from the perspective of pilot operation. First, according to the principle of flight mechanics, the attitude adjustment model is established for the horizontal direction of the approach process, and the pilot’s operation model for various position errors is based on the concept of the stochastic process. This attitude adjustment model can replicates the process of the pilot operating the steering column to change the aircraft’s attitude. When combined with the pilot’s operation model, it is possible to simulate the position errors generated during the approach process. Building on this, the horizontal overlapping conditions of two aircraft are analyzed to simulate the horizontal overlap process in the paired approach. The duration and instances of overlap counted and the ratio between these results and the total running time give the overlap probability and frequency. Multiple simulations in MATLAB reveal that higher pilot operating accuracy shortens the time for the aircraft to align with the course, whereas lower accuracy leads to unstable horizontal position errors. Furthermore, the horizontal overlap in paired approaches primarily occurs at the beginning of the procedure, and enhancing the pilot’s operating accuracy does not significantly affect the probability and frequency of horizontal overlap.

This work presents a numerical analysis for exploring heat transfer phenomena in an enclosed cavity using magnetohydrodynamics natural convection. Because of the numerous real-world applications of nanofluids and hybrid nanofluids in industrial and thermal engineering developments, hybrid nanofluids are used as fluid mediums in the fluid field. A hexagonal-shaped heat exchanger is taken with two circular surfaces along the middle part. The upright circular surface acts as a homogeneous heat source, while the lower circular surface functions as a heat sink. The remaining portions of the adjacent walls are thermally insulated. The copper (Cu) and titanium dioxide (TiO₂) nanoparticles are suspended into water to make a hybrid nanofluid. For solving the corresponding governing equations, the weighted-residual finite element method is applied. To explain the major outcomes, isotherms, streamlines, and many others 2D and 3D contour plots are involved graphically with a physical explanation for different magnitudes of significant parameters: Rayleigh number , Hartmann number , and nanoparticle volume fraction . The novelty of this work is to apply response surface methodology on the natural convective hybrid nanofluid model, to visualize 2D and 3D effects, and to study the sensitivity of independent parameters on response function. Due to the outstanding thermal properties of the hybrid nanofluid, the addition of Cu and TiO₂ nanoparticles into H₂O develops the heat transfer rate to 35.85% rather than base fluid. Moreover, a larger magnitude of Ra and the accumulation of mixture nanoparticles result in the thermal actuation of a hybrid nanofluid. With greater magnetic impact, an opposite response is exhibited.

This paper proposes a model predictive speed control strategy for a surface-mounted permanent magnet synchronous motor by applying Laguerre functions. The model predictive controller (MPC) incorporates an integrator. A quadratic programming procedure is applied to solve the constrained optimization problem online. The paper also provides a solution for stability. The performance efficiency of the proposed scheme is validated by comparing the results with the performance of an optimal linear quadratic regulator, conventional state-space model predictive control, and a simple MPC algorithm with integral action. Extensive simulation results confirm the efficacy of the proposed scheme, showing that it achieves good steady-state performance while maintaining a fast dynamic response.