A method is introduced for the identification of the nonlinear governing equations of dynamical systems in the presence of discontinuous and nonsmooth nonlinear forces, such as the ones generated by frictional contacts, based on noisy measurements. The so-called Physics Encoded Sparse Identification of Nonlinear Dynamics (PhI-SINDy) builds upon the existing RK4-SINDy identification scheme, incorporating known physics and domain knowledge in three different ways (biases). In this way, it addresses the discontinuous behavior of frictional systems when stick–slip phenomena are observed, which can not be captured by existing state-of-the-art approaches. The potential of PhI-SINDy is highlighted through a plethora of case studies, starting from a simple yet representative Single Degree of Freedom (SDOF) oscillator with a Coulomb friction contact under harmonic load, using both synthetic and experimental noisy measurements. An alternative friction law, namely the Dieterich-Ruina one, is also considered as well as a more realistic excitation time series, which was generated based on the Jonswap spectrum. Lastly, a Multi Degree of Freedom system with single and multiple friction contacts is used as a testbed, showcasing the applicability of PhI-SINDy to more complicated systems and/or multiple sources of discontinuous nonlinearities.

A key computational challenge in maintenance planning for deteriorating structures is to concurrently secure (i) optimality of decisions over long planning horizons, and (ii) accuracy of realtime parameter updates in high-dimensional stochastic spaces. Both are often encumbered by the presence of discretized continuous-state models that describe the underlying deterioration processes, and the emergence of combinatorial decision spaces due to multi-component environments. Recent advances in Deep Reinforcement Learning (DRL) formulations for inspection and maintenance planning provide us with powerful frameworks to handle efficiently near-optimal decision-making in immense state and action spaces without the need for offline system knowledge. Moreover, Bayesian Model Updating (BMU), aided by advanced sampling methods, allows us to address dimensionality and accuracy issues related to discretized degradation processes. Building upon these concepts, we develop a joint framework in this work, coupling DRL, more specifically deep Q-learning and actor-critic algorithms, with BMU through Hamiltonian Monte Carlo. Single- and multi-component systems are examined, and it is shown that the proposed methodology yields reduced lifelong maintenance costs, and policies of high fidelity and sophistication compared to traditional optimized time- and condition-based maintenance strategies.