Constrained Performance-Based Optimization of T-NES: A Stochastic Polynomial Chaos Expansion approach with Far-Field and Near-Field considerations

This paper proposes a reliability-constrained Performance-Based Design Optimization (PBDO) framework for Track Nonlinear Energy Sinks (T-NESs) that integrates Stochastic Polynomial Chaos Expansion (SPCE)-based fragility modeling, dual-hazard seismic representation, and life-cycle cost optimization within a unified probabilistic framework. Existing probabilistic optimization approaches for T-NES devices typically rely on lognormal fragility assumptions combined with first-passage formulations, requiring quasi-stationary excitation models that are unsuitable for representing pulse-like Near-Field (NF) earthquakes. The proposed methodology introduces three main contributions. First, SPCE is embedded directly within the optimization loop to construct fragility functions from peak Engineering Demand Parameters (EDPs), eliminating predefined distributional assumptions while reducing the computational cost of fragility construction by approximately a factor of eight compared with conventional Monte Carlo-based procedures. Second, the peak-response formulation eliminates the quasi-stationary excitation requirement inherent to first-passage approaches, enabling consistent treatment of both Far-Field (FF) and NF ground motions within the same optimization framework. Third, the design problem is formulated as a dual-hazard reliability-constrained optimization, in which expected life-cycle cost is minimized under FF seismic demand while a probabilistic stroke constraint is enforced under NF excitation to ensure device operability during pulse-like events. The framework is demonstrated on a mid-rise steel frame located in Concepción, Chile. Results indicate that unconstrained economic optimization marginally violates the target stroke reliability under NF excitation. Enforcing the constraint increases optimal device damping by approximately 35% while raising expected life-cycle cost by only 1.6%, quantifying the limited economic trade-off required to guarantee robustness. Validation against recorded FF and NF ground motions confirms interstory drift reductions of up to 68% under FF events while maintaining stroke demands within the prescribed admissible limits under the most demanding NF pulses. The proposed framework provides a computationally efficient methodology for reliability-constrained optimization of nonlinear seismic absorbers while explicitly accounting for the fundamentally different roles of FF and NF ground motions in structural performance and device reliability.