Bolts have the advantages of simple installation and easy removal. They are widely applied in aerospace and high-speed railway traffic. However, the loosening of bolts under mixed loads can lead to nonlinear decreases in pre-loading. This affects the safety performance of the structure and may lead to catastrophic consequences. Existing techniques cannot be used to monitor the bolt performance status in time. This has caused significant problems with the safety and reliability of equipment. In order to study the relaxation law of bolt pre-loading, this paper carries out an experimental analysis for 8.8-grade hexagonal bolts and calibrates the torque coefficient. We also studied different loading waveforms, nickel steel plate surface roughnesses, tangential displacement frequencies, four different strengths and bolt head contact areas of the bolt, the initial pre-loading, and the effects of tangential cyclic displacement on pre-loading relaxation. This was done in order to accurately predict the degree of bolt pre-loading loosening under external loads. The laws are described using the allometric model function and the nine-stage polynomial function. The least squares method is used to identify the parameters in the function. The results show that bolts with a smooth surface of the connected structure nickel steel flat plate, high-frequency working conditions, half-sine wave, and a high-strength have better anti-loosening properties. Taking 5–10 cycles of cyclic loading as a boundary, the pre-loading relaxation is divided into two stages. The first stage is a stage of rapid decrease in bolt pre-loading, and the second stage is the slow decrease process. The performance prediction study shows that the allometric model function is the worst fitted, at 71.7% for the small displacement condition. Other than that, the allometric model function and the nine-stage polynomial function can predict more than 85.5% and 90.4%, which require the use of least squares to identify two and ten unknown parameters, respectively. The complexity of the two is different, but both can by better indicators than the pre-loading relaxation law under specific conditions. It helps to improve the monitoring of bolt loosening and the system use cycle, and it can provide theoretical support for complex equipment working for a long time.

As the low-altitude economy develops rapidly, precise radar altimetry is crucial for ensuring the safety and reliability of drone flights. In the context of urban radio detection, the presence of numerous buildings and ground surfaces gives rise to electromagnetic wave multipath propagation. This objective factor gives rise to errors in radar altimetry. Existing channel models often lack the intricate details required to accurately quantify multipath error mechanisms in kilometer-scale complex electromagnetic environments. Therefore, there is an urgent need for a high-fidelity simulation framework. The present study has put forward a pioneering approach to radio altimetry simulation and accuracy assessment in intricate urban environments. The objective of this study is to investigate the impact of multipath propagation on radar altimetry precision. The present study has proposed a novel integration of radar altimetry simulation with kilometre-scale urban electromagnetic simulation models. The simulation of echo signals has been achieved through the utilization of the shooting and bouncing rays (SBR) method and inverse fast Fourier transform (IFFT). A comparative analysis has been conducted based on ranging results from radar systems for different urban models, thereby enabling a mechanism analysis of factors affecting radar altimetry. The study has demonstrated that increased building density and height, along with reduced elevation angles during altimetry, exacerbate ranging errors.