The existence of fractures has a significant influence on the mechanical properties of a rock mass. The sensitivity of the rock mass’s mechanical properties to the fracture’s geometric parameters is conducive to improving the measurement accuracy of fractured rock mass engineering. Firstly, the fracture geometric parameters in the dam site area of Lianghekou Hydropower Station were counted using the ShapeMetriX^3D system. Then, the effect of the fracture’s geometric parameters on the deformation characteristics, failure mode, and mechanical parameters of the rock mass were investigated based on the RFPA^3D under the uniaxial compression test. The results showed that the stress–strain curves of the fractured rock mass mainly exhibited elastic-brittle characteristics. The failure pattern of the fractured rock mass was mainly defined by a compressive-shear composite. Additionally, the influence of the fracture’s geometric parameters on the uniaxial compressive strength (UCS) was greater than that of elastic modulus. The sensitivity of the UCS to fracture trace length was more significant.

Aero-engine turbine components have complex structures, harsh service load environments, and strong nonlinear structural responses, so it is difficult to establish the explicit limit state function, which is a typical nonlinear implicit function reliability analysis problem. To address this challenge, based on Particle Swarm Optimization and a Back Propagation Neural Network (PSO-BPNN), a reliability analysis approach is proposed in this paper. In the proposed method, the PSO algorithm is employed to optimize the initial weights and biases of the BPNN. This global optimization capability prevents the neural network from falling into local extrema and mitigates overfitting, thus improving the accuracy and generalization of the BPNN in approximating implicit limit state functions. On this basis, the Monte Carlo simulation (MCS) method is used to call the established neural network to calculate the failure probability, and the original implicit limit state function is not needed at this time. The proposed PSO-BPNN approach exhibits higher computational precision and efficiency, particularly for problems with strong nonlinearity and high dimensionality. Numerical examples are used to verify the efficiency and accuracy of the proposed approach, which is further applied to analyze the reliability of an aero-engine turbine casing structure. The results demonstrate that the proposed method not only offers high computational efficiency and accuracy but also provides significant advantages in handling complex nonlinear implicit reliability analysis problems. This indicates its strong potential to serve as a reliable and practical tool for engineering reliability analysis, particularly in the aerospace domain, where structural components often operate under extreme conditions.

To effectively determine the influences of fuzzy uncertainties on structural systems in engineering, according to the fuzzy failure probability (FFP) model, which is based on the probabilistic perspective, the importance measure (IM) technique is extended to fuzzy uncertain structural systems. A novel IM framework, i.e., the fuzzy-failure-probability-based IM (FFP-IM), is established. By transforming the fuzzy failure probability into the expected value of the function for the failure domain, the proposed FFP-IM index can be represented as the variance-based IM of that index function. Then, an efficient solution algorithm for the proposed FFP-IM index is established based on the state-dependent parameter method. Ultimately, the Ishigami function, alongside three practical engineering examples, validates the proposed FFP-IM’s rationality and applicability. Furthermore, these examples illustrate the solution algorithm’s superior computational efficiency and accuracy.