Zhiping Qiu

The symplectic algorithm for Hamiltonian systems is renowned for its high accuracy and efficiency in long‐term computations. However, its direct application to non‐conservative problems in engineering dynamics is limited by the presence of dissipative effects and external load terms. To overcome these challenges, this paper presents a novel symplectic precise integration method based on the perturbation series approach, specifically tailored for structural dynamic response problems. By introducing a state vector, the general structural dynamic response equation is reformulated into a generalized Hamiltonian framework. Subsequently, perturbation theory is applied to transform this generalized Hamiltonian equation into a sequence of linear Hamiltonian equations, effectively converting the problem of solving non‐conservative equations into one of solving multiple conservative equations. The precise integration method is then used to derive a step mapping matrix that significantly improves accuracy without substantially increasing computational cost. Numerical examples are provided to highlight the efficacy and practical applicability of the proposed method in addressing complex structural dynamic response problems.

As a classical design method for addressing uncertainty in control systems, robust control is designed with the goal of complete reliability of the control system. Nevertheless, the pursuit of robustness can inadvertently give rise to considerable performance degradation, rendering the resultant closed-loop control system excessively conservative in its design. Reliability-based design methods serve as an effective approach for managing uncertainties, which will achieve a balance between the robustness and performance of the active control system by taking advantage of the characteristic of reliability that allows for a certain level of permissible failure probability. The accurate quantification of uncertainty is the key to achieving reliable control, but common uncertainty quantification methods cannot achieve credible quantification of uncertainty in small samples and update the distribution of new samples. In this paper, a nonprobabilistic Bayesian inference based interval uncertainty quantification method is proposed. This method updates the distribution of interval boundaries and radii by introducing a small number of samples, and obtains interval parameters under a given confidence level. On the basis of uncertainty quantification, the dynamic reliability of the vibration system is derived, and nonprobabilistic reliability is introduced into the design of active controllers through optimization strategies. The reliable control strategy aims to select the optimal controller parameters on a reliable path with a given credibility, in order to solve the problem of overly conservative robust control theory. Two numerical examples were used to verify the feasibility and applicability of this method.