Abstract
Disruptions to high-speed rail (HSR) can cause passenger-service losses across cities, while air alternatives depend on transfers and residual capacity. This study evaluates functional robustness in an HSR-centered rail–air network and selects city-level hardening investments under uncertain disruption probabilities. A time-expanded multiplex represents scheduled services, shared enabling components, correlated damage, restoration, and capacity-constrained passenger reassignment. A two-stage Wasserstein distributionally robust optimization (DRO) model minimizes worst-case mean–conditional value-at-risk (CVaR) loss. A decomposition framework is presented for continuous restoration. A reproducible semi-synthetic benchmark with 40 cities and 21 scenarios uses screened exhaustive search and monotone recourse closure. With a four-city budget, nominal planning protects Beijing, Hangzhou, Hefei, and Nanjing, whereas DRO protects Beijing, Shanghai, Guangzhou, and Nanjing. Worst-case mean–CVaR robustness increases from 83.86% to 89.37%, while nominal mean robustness decreases from 96.07% to 95.02%. At each portfolio’s joint worst-case mean–CVaR distribution, 90% CVaR robustness increases from 69.71% to 85.13%. These controlled results illustrate how probability ambiguity changes hardening priorities and the trade-off between nominal performance and adverse-distribution risk. Operational application requires observed timetables, demand, capacities, recovery resources, and hazard frequencies.