This paper investigates the influence of microscopic features on the tooth surface of a geared rotor-bearing system on the system’s dynamic behavior. First, by upgrading the Weierstrass–Mandelbrot function to redefine the gear backlash equation and combining this with a nonlinear dynamic model of a geared system, an improved nonlinear dynamic model is established. Second, the effects of four crucial model parameters on the gear dynamics are examined through a series of numerical simulations, allowing us to explore the corresponding dynamic response and the model’s feasibility. The results show that surface roughness plays a significant role in the dynamic behavior of the gears, with lower surface roughness corresponding to better dynamic performance. The fractal dimension is found to be a non-negligible factor with respect to gear dynamics, and decreasing the fractal dimension proves advantageous to the dynamic response. As the stiffness coefficient decreases and the gear meshing damping increases, the stability of the system improves. Finally, the model is validated through a comparison of our theory with experimental data and another certified model. Our theory constructs a mathematical relationship between the gear dynamics and tooth surface micro-characteristics, forming a basis for future tooth surface topographies as well as a reference for the dynamic analysis of other highly paired systems.

The anti-lock braking system (ABS) is an essential part in ensuring safe driving in vehicles. The Security of onboard safety systems is very important. In order to monitor the functions of ABS and avoid any malfunction, a model-based methodology with respect to structural analysis is employed in this paper to achieve an efficient fault detection and identification (FDI) system design. The analysis involves five essential steps of SA applied to ABS, which includes critical faults analysis, fault modelling, fault detectability analysis and fault isolability analysis, Minimal Structural Over-determined (MSO) sets selection, and MSO-based residual design. In terms of the four faults in the ABS, they are evaluated to be detectable through performing a structural representation and making the Dulmage-Mendelsohn decomposition with respect to the fault modelling, and then they are proved to be isolable based on the fault isolability matrix via SA. After that, four corresponding residuals are generated directly by a series of suggested equation combinations resulting from four MSO sets. The results generated by numerical simulations show that the proposed FDI system can detect and isolate all the injected faults, which is consistent with the theoretical analysis by SA, and also eventually validated by experimental testing on the vehicle (EcoCAR2) ABS.