A Galerkin/neural approach for the stochastic dynamics analysis of nonlinear uncertain systems

The paper presents a Galerkin/neural approach (GNa) for the dynamics analysis of nonlinear mechanical systems affected by parameter randomness. In the specialised literature various procedures are nowadays available to evaluate the response statistics of such systems, but a choice has sometimes to be done between simple methods (that often provide unreliable solutions) and other more complex methods (where accurate solutions are provided with a heavy computational effort). The proposed method, where a Galerkin approach is combined with a neural one (basically an expansion of RBF for the approximation of the system response) could be a valid alternative to the classical procedures. Furthermore the proposed Galerkin/neural approach introduces an error parameter which can provide an effective criterion to accept or refuse the obtained approximate solution. To validate the proposed approach several nonlinear systems with random parameters are introduced as case studies, and the results (main moments of the response process) are compared with Monte Carlo Simulation (MCS).

Figure 1. System response (rotation θθ) at different instants (2, 5, 10 and 15 sec): comparison between MCS and Galerkin/neural approach (GNa) approximation (Nφ=5)(Nφ=5). Figure 2. Mean value (rotation θθ): comparison between MCS and Galerkin/neural approach (GNa) results (Up) (Nφ=5)(Nφ=5); Standard deviation (rotation θθ): comparison between MCS and GNa results (Down) (Nφ=5)(Nφ=5). Figure optionsDownload as PowerPoint slideFigure optionsDownload as PowerPoint slideHighlights
► Uncertainties may lead to large and unexpected excursion of the structural response.
► Approximation of the random system response by means of an expansion of radial basis functions (RBF).
► Evaluation of the committed error in a Galerkin projection schema (a posteriori control parameter).