It is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method.

Estimating system reliability has been recognized as a critical step in reliability-based design optimization for structural systems. The estimation of system reliability entails multi-dimensional integration, which is very difficult and numerically expensive. The proposed hybrid method integrates the concepts of saddlepoint approximation, the dimension reduction method (DRM) and copulas. The moment-based saddlepoint approximation enhanced by the DRM is used to calculate the component reliability. The copula method is adopted to realize the joint failure probability modelling between two failure modes. Reliability-based sensitivity analysis for the reliability-based robust design optimization is carried out as well. The structural system optimization model is established, including the Euclid norm of the reliability sensitivity as an optimization objective and system reliability as a constraint. Examples demonstrate that the optimization results obtained by the proposed approach ensure the maximization of the robustness of the structural system.

In order to efficiently solve a forward kinematics of parallel manipulators for real-time applications, a Jacobian free monotonic descent algorithm is proposed in this article. The system of nonlinear equations of a specified 6-degree-of-freedom parallel manipulator is established using a geometric analysis method. The proposed Jacobian free monotonic descent algorithm is modified using a traditional Newton–Raphson method by employing a first-order Taylor series expansion to numerically approximate a Jacobian matrix. A monotonic descent factor is employed for preventing the iteration from divergence even with poor initial conditions. The proposed algorithm inherits the merits of the Newton–Raphson algorithm and overcomes its drawbacks. The Jacobian free monotonic descent algorithm is programmed in MATLAB/Simulink and then is compiled to a real-time PC system with xPC target technology for implementation. The experimental results demonstrate that the proposed Jacobian free monotonic descent algorithm is effective and feasible for the real-time forward kinematics of parallel manipulators in terms of accuracy, convergence, and execution time

Surface wear is one of the major causes of damage to wire ropes in multilayer winding systems. This damage leads to performance degradation and affects the service safety of wire rope. To reveal the wear evolution and the performance degradation of wire rope in service, the correlations between the wear characteristic parameters and the residual strength were investigated. The results show that the variation in the wear parameters is affected by the wear distribution and the structure of the wire rope. The main wear mechanisms between wire ropes are adhesion wear and abrasive wear. Different wear parameters should be combined to evaluate the wear state of the wire rope. The tensile temperature rise could accurately reflect the wear evolution of the in-service wire rope under the condition of a large wear degree. The negative correlation between the residual strength and the wear area of the damaged rope samples is the strongest.