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Purpose – The purpose of this paper is to develop a new formulation using spectral approach, which can predict the wave behavior to uncertain parameters in mid and high frequencies. Design/methodology/approach – The work presented is based on a hybridization of a spectral method called the “wave finite element (WFE)” method and a non-intrusive probabilistic approach called the “polynomial chaos expansion (PCE).” The WFE formulation for coupled structures is detailed in this paper. The direct connection with the conventional finite element method allows to identify the diffusion relation for a straight waveguide containing a mechanical or geometric discontinuity. Knowing that the uncertainties play a fundamental role in mid and high frequencies, the PCE is applied to identify uncertainty propagation in periodic structures with periodic uncertain parameters. The approach proposed allows the evaluation of the dispersion of kinematic and energetic parameters. Findings – The authors have found that even though this approach was originally designed to deal with uncertainty propagation in structures it can be competitive with its low time consumption. The Latin Hypercube Sampling (LHS) is also employed to minimize CPU time. Originality/value – The approach proposed is quite new and very simple to apply to any periodic structures containing variabilities in its mechanical parameters. The Stochastic Wave Finite Element can predict the dynamic behavior from wave sensitivity of any uncertain media. The approach presented is validated for two different cases: coupled waveguides with and without section modes. The presented results are verified vs Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Purpose – Physical phenomena interact with each other in ways that one cannot be analyzed without considering the other. To account for such interactions between multiple phenomena, partitioning has become a widely implemented computational approach. Partitioned analysis involves the exchange of inputs and outputs from constituent models (partitions) via iterative coupling operations, through which the individually developed constituent models are allowed to affect each other’s inputs and outputs. Partitioning, whether multi-scale or multi-physics in nature, is a powerful technique that can yield coupled models that can predict the behavior of a system more complex than the individual constituents themselves. The paper aims to discuss these issues. Design/methodology/approach – Although partitioned analysis has been a key mechanism in developing more realistic predictive models over the last decade, its iterative coupling operations may lead to the propagation and accumulation of uncertainties and errors that, if unaccounted for, can severely degrade the coupled model predictions. This problem can be alleviated by reducing uncertainties and errors in individual constituent models through further code development. However, finite resources may limit code development efforts to just a portion of possible constituents, making it necessary to prioritize constituent model development for efficient use of resources. Thus, the authors propose here an approach along with its associated metric to rank constituents by tracing uncertainties and errors in coupled model predictions back to uncertainties and errors in constituent model predictions. Findings – The proposed approach evaluates the deficiency (relative degree of imprecision and inaccuracy), importance (relative sensitivity) and cost of further code development for each constituent model, and combines these three factors in a quantitative prioritization metric. The benefits of the proposed metric are demonstrated on a structural portal frame using an optimization-based uncertainty inference and coupling approach. Originality/value – This study proposes an approach and its corresponding metric to prioritize the improvement of constituents by quantifying the uncertainties, bias contributions, sensitivity analysis, and cost of the constituent models. [ABSTRACT FROM AUTHOR]

Purpose - Optimization under a deterministic approach generally leads to a final design in which the performance may degrade significantly and/or constraints can be violated because of perturbations arising from uncertainties. The purpose of this paper is to obtain a better strategy that would obtain an optimum design which is less sensitive to changes in uncertain parameters. The process of finding these optima is referred to as robust design optimization (RDO), in which improvement of the performance and reduction of its variability are sought, while maintaining the feasibility of the solution. This overall process is very time consuming, requiring a robust tool to conduct this optimum search efficiently. Design/methodology/approach - In this paper, the authors propose an integrated tool to efficiently obtain RDO solutions. The tool encompasses suitable multiobjective optimization (MO) techniques (encompassing: Normal-Boundary Intersection, Normalized Normal-Constraint, weighted sum method and min-max methods), a surrogate model using reduced order method for cheap function evaluations and adequate procedure for uncertainties quantification (Probabilistic Collocation Method). Findings - To illustrate the application of the proposed tool, 2D structural problems are considered. The integrated tool prove to be very effective reducing the computational time by up to five orders of magnitude, when compared to the solutions obtained via classical standard approaches. Originality/value - The proposed combination of methodologies described in the paper, leads to a very powerful tool for structural optimum designs, considering uncertainty parameters, that can be extended to deal with other class of applications. [ABSTRACT FROM AUTHOR]