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

## TL;DR

This paper introduces an efficient numerical method to accurately predict extreme response statistics of nonlinear structural systems under stochastic loads, with applications to ocean engineering, enabling optimized mitigation strategies.

## Contribution

A novel numerical approach combining statistical linearization and effective measures for fast, accurate extreme response prediction in nonlinear systems under stochastic excitation.

## Key findings

- The method captures heavy-tail response statistics orders of magnitude faster than direct simulations.
- Optimized asymmetric nonlinear springs outperform traditional linear dampers and cubic energy sinks.
- Application to ocean engineering systems demonstrates effective mitigation of extreme events.

## 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, piecewise 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.