Extreme events and their optimal mitigation in nonlinear structural systems excited by stochastic loads: Application to ocean engineering systems

Abstract

We develop an efficient numerical method for the probabilistic quantification of the response statistics of nonlinear multi-degree-of-freedom structural systems under extreme forcing events, emphasizing accurate heavy-tail statistics. The response is decomposed to a statistically stationary part and an intermittent component. The stationary part is quantified using a statistical linearization method while the intermittent part, associated with extreme transient responses, is quantified through i) either a few carefully selected simulations or ii) through the use of effective measures (effective stiffness and damping). The developed approach is able to accurately capture the extreme response statistics orders of magnitude faster compared with direct methods. The scheme is applied to the design and optimization of small attachments that can mitigate and suppress extreme forcing events delivered to a primary structural system. Specifically, we consider the problem of suppression of extreme responses in two prototype ocean engineering systems. First, we consider linear and cubic springs and perform parametric optimization by minimizing the forth-order moments of the response. We then consider a more generic, possibly asymmetric, piece-wise linear spring and optimize its nonlinear characteristics. The resulting asymmetric spring design far outperforms the optimal cubic energy sink and the linear tuned mass dampers.Keywords Impact mitigation in nonlinear structural systems; Response under extreme events; Optimization and design under stochastic loads; Nonlinear Energy Sinks; Optimization of suspended seats and decks in high speed craft motion.

Heavy-Tailed Response of Structural Systems Subjected to Stochastic Excitation Containing Extreme Forcing Events

“…In such cases, it is usually not feasible to run Monte Carlo simulations for various parameter sets during the design process owing to the computational costs associated with low probability rare events, let alone perform parametric optimization. In different work [41], we demonstrate application of the method to design and optimization in ocean engineering applications and show that the approach is well suited to predict optimal extreme-event mitigating designs and for system reliability. Thus, we can obtain the following conditionally background variances:…”

“…An important difference in the overdamped scenario is that the system does not exhibit oscillatory response, hence we directly operate on the response instead of the envelope of the response. (37) and we obtain the following pdf for the displacement of the system: (41) and this gives the following result for the acceleration pdf: Note that here, we do not have the simple scaling as in the underdamped case for the conditionally rare component of the pdf.…”

“…The systems considered in this work are linear; however, the general method is directly applicable to nonlinear structural systems (see Ref. [41] for nonlinear systems).…”

Stochastic reduced-order models for stable nonlinear ordinary differential equations

“…where the process W (t) is known as the hysteresis response of the Bouc-Wen oscillator. Finally, the last system solved as an example for the proposed methodologies is the two-degree-of-freedom (2DOF) nonlinear energy sink (NES) system [57], used for the reduction of the response of ocean-engineering systems subjected to extreme loading [58], whose state is described by the bi-variate stochastic process…”

Extreme Events: Mechanisms and Prediction

“…The real-time prediction of the extreme events, on the other hand, informs the optimal time for the activation of the control strategy (see figure 1). The mitigation of extreme events within a dynamical systems framework has only recently been examined [26,27,28,29,30,31]. The research in this direction has been limited to mitigation in simplified models by introducing arbitrary perturbations that nudge the system away from the extreme events.…”