Response Statistics of Linear Structures With Uncertain-but-Bounded Parameters Under Gaussian Stochastic Input

Abstract

Uncertainty plays a fundamental role in structural engineering since it may a®ect both external excitations and structural parameters. In this study, the analysis of linear structures with slight variations of the structural parameters subjected to stochastic excitation is addressed. It is realistically assumed that su±cient data are available to model the external excitation as a Gaussian random process, while only fragmentary or incomplete information about the structural parameters are known. Under this assumption, a nonprobabilistic approach is pursued and the°uctuating properties are modeled as uncertain-but-bounded parameters via interval analysis. A method for evaluating the lower and upper bounds of the second-order statistics of the response is presented. The proposed procedure basically consists in combining random vibration theory with¯rst-order interval Taylor series expansion of the mean-value and covariance vectors of the response. After some algebra, the sets of¯rst-order ordinary di®erential equations ruling the nominal and¯rst-order sensitivity vectors of response statistics are derived. Once such equations are solved, the bounds of the mean-value and covariance vectors of the response can be evaluated by handy formulas.To validate the procedure, numerical results concerning two di®erent structures with uncertain-but-bounded sti®ness properties under seismic excitation are presented.

Interval Dynamic Response of Discretized Structures With Uncertain-but-Bounded Parameters

“…According to the improved interval analysis [10], the i-th real interval variable I i can be written in the following affine form [18]:…”

“…where ˆ1,1 I i e is the so-called Extra Unitary Interval (EUI) [10]; 0,i is the midpoint value (or mean) and i denotes the deviation amplitude (or radius), defined, respectively, as:…”

“…Subsequently, the Interval Perturbation Method (IPM), which is based on Taylor series expansion and parameter perturbation, has been introduced to evaluate the interval dynamic response of structures subjected to deterministic [6][7][8][9] or stochastic excitations [10]. More recently, Gao et al [11] presented the interval factor method to calculate the dynamic response of truss structures.…”

Dynamic analysis of wind turbine gearboxes with unknown‐but‐bounded parameters under random wind excitation

“…Some attentions have been paid to study the dynamic behaviours of the mechanical system with uncertain but bounded parameters subjected to random excitations. To predict the bounds of statistical properties for responses of linear structural systems, Muscolino and Sofi [25] combined the linear random vibration theory with the first‐order interval Taylor series expansion of the mean and covariance vectors. However, this method was limited for slight variations of system parameters.…”

Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

“…Thus, to construct a hybrid framework which integrates the merits of both methods for the hybrid uncertain engineering problems with random and non-probabilistic parameters simultaneously is desirable. The stochastic interval responses of structures with uncertain-but-bounded parameters under random excitation have been investigated in literatures [28][29][30]. The random interval analysis technique for the hybrid uncertain structure with random and interval parameters have been studied by Gao et al [31].…”