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Interval analysis of structures using an improved particle swarm optimization method

Nowadays, deterministic models are mostly used in both static and dynamic analyses of structures, in which all structural parameters are assumed having exactly known values. However, these values could not be predicted precisely in real engineering situations. They are diffusedly affected by inaccurate measurements, manufacturing errors, material defects, and changes of environment. Simply ignoring these intrinsic unpredictable natures may cause excessive approximations and the computed results could be far off the real ones. There is no doubt that these uncertainties need to be accounted for accurate predictions of structural static and dynamic responses. Probabilistic approaches are one of the traditional approaches to handle uncertain problems. Probabilistic analysis has been extensively developed in the last few decades, which is reliable and accurate only when sufficient and correct statistical information of all random variables is available. There is a risk that even small errors in probabilistic data may cause large errors in calculated probabilities of failure. Furthermore, the wealthy information of variables is not always accessible in engineering practice, especially at the initial stage of the analysis and design. Therefore, non-probabilistic approaches are becoming increasingly popular to solve uncertain problems. Interval method, which just requires the upper and lower bounds of uncertain variables, is one of the dominants. Optimization methods have also started to be utilized to solve interval uncertain problems and obtain exact changes ranges of system outputs. The minimum and maximum results of optimization problems are corresponding to the lower and upper bounds of system outputs respectively. This paper presents both static analysis and dynamic characteristic analysis of structures with interval physical parameters. The mathematical models for minimising and maximising structural displacements and natural frequencies are developed. A low-discrepancy sequence initialized particle swarm optimization method with high-order nonlinear time-varying inertia weight (LHNPSO) is employed to solve the optimization problems. Two sharp bounds of structural displacements in static analysis and natural frequencies in dynamic analysis are determined. The effectiveness of the proposed methods is illustrated through truss and frame structures. Monte Carlo simulation method (MCSM) is also implemented to verify the accuracy of the results.