Distributional shift safety margin for machine learning models in structural engineering

Safety-critical engineering deployments routinely face performance deterioration under dataset shift, yet post-hoc, label-free safeguards that work without retraining remain scarce. The Distributional Shift Safety Margin (DSSM) is presented as a model-agnostic, deployment-time offset that quantitatively suppresses unsafe over-estimation when covariate shift is detected. DSSM requires only unlabelled deployment features and the model’s training-time predictive spread; the margin is scaled by a kernel two-sample distance between training and deployment distributions (Maximum Mean Discrepancy, MMD) and a user-set unsafe-rate target \(\alpha \) . The optimal margin is characterised in closed form as the \((1-\alpha )\) -quantile of the deployment error distribution; the practical estimator is a label-free MMD-based plug-in surrogate motivated by an RKHS+Cantelli argument under stated assumptions, and is empirically conservative relative to the optimum. The framework is validated on two real engineering datasets: the UCI Concrete Compressive Strength benchmark ( \(n=1030\) ) and the NIMS Steel Fatigue Strength dataset ( \(n=437\) , 25 features). Controlled covariate-shift scenarios are constructed from held-out real measurements by selection-bias resampling and mild affine perturbation; these are designed to be physically plausible probes rather than recordings of naturally occurring operational drift, and the full evaluation is repeated under 15 independent RNG seeds to give error bars rather than point estimates. Across both case studies and three model architectures (Random Forest, Gradient Boosting, Ridge), DSSM at \(\alpha =1\%\) drives the deployment unsafe rate to 0.0% from baseline rates of 5–12%, with transparent and tunable MAE penalties that scale with target variance and shift magnitude. DSSM is benchmarked against modern conformal-prediction baselines (split, weighted, CQR), which produce somewhat tighter thresholds when labelled calibration data are available. A regime-conditioned extension addresses heteroscedasticity by computing per-regime margins from local \(\sigma _P^{(k)}\) and local MMD \(^2_k\) , and is shown to reduce the deployment MAE penalty by 44–49% relative to the global construction while preserving the safety target. Sensitivity studies confirm robustness to kernel choice and bandwidth selection. DSSM complements contemporary AI risk-management guidance as a lightweight “measure-to-manage” control mechanism that engineering practitioners can tune, audit, and justify when deploying machine-learning surrogates in safety-critical applications.