Considering that uncertainty is inherent and unavoidable in engineering practice and the available information about the uncertain parameters is always not sufficient, the paper tries to carry out the nonprobabilistic vibration reliability analysis so as to avoid resonance on uncertain structure with bounded parameters. The input uncertain-but-bounded parameters are treated as interval variables, and an interval model is adopted to describe bounded uncertainties. Then a theory of nonprobabilistic reliability is introduced, in which the dimensionless nonprobabilistic reliability index and system reliability index are defined. In order to investigate the resonance failure with reliability method, the resonance failure domains are stated according to the relationships between the natural frequencies and the excitation frequencies. Then the uncertain structure is modeled as a series system and a system reliability index is proposed to evaluate the safety of the structure. The paper also takes a frequency analysis on the uncertain space beam structure to get the resonance failure modes. A frequency analysis method based on the monotonicity discriminant of the frequency sensitivity is presented. Then an optimization algorithm is introduced to verify the validity of the former frequency analysis method. Two examples are provided to illustrate the effectiveness and feasibility of the presented method.
Abstract. The paper aims at the frequency analysis problem of the uncertain structure, takes the space beam structure with interval parameters as the research object. An expression of the relationship between the structural natural frequencies and the interval parameters is presented. With the partial derivative of the frequency in this expression, the frequency sensitivity of interval parameters is obtained. On the basis, a frequency analysis method is presented which built on the discriminant of the sensitivity monotonicity. Use this method, a frequency analysis is carried on a simplified GARTEUR plane model. The method is then verified by using an optimization algorithm. The frequency analysis method presented in this paper has a certain theoretical and practical significance in the dynamic analysis of uncertain structure.
System reliability allocation is an important ingredient in system reliability design, and it is also a decision-making issue of reliability engineering. To achieve the optimization of system reliability allocation, an optimization model for system reliability allocation, which takes the system cost as the objective function, is constructed through the general cost function. In order to overcome the shortcomings of particle swarm optimization (PSO) appearing in reliability allocation optimization, the premature and/or slow speed of convergence in later period, the sequential quadratic programming (SQP) was introduced to improve the PSO algorithm. The algorithm uses PSO as the global optimizer while the SQP is employed for accelerating the local search. Thus, the particles are able to search the whole space while searching for local optimization fast, which not only assures the convergence of the algorithm, but also increases the probability of obtaining the global optimum. Applied the algorithm to the problem of system reliability allocation, the simulation results show that it has excellent global search capability and provides rational optimization results compared to the existing approaches.
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