Uncertainty quantification (UQ) is the discipline of characterizing, propagating, and reducing uncertainty in computational models and engineering predictions. It provides a rigorous framework for making decisions under uncertainty, which is fundamental to modern earthquake engineering.
Uncertainty quantification (UQ) is the discipline of identifying, characterizing, propagating, and reducing uncertainty in computational models and predictions. Every engineering prediction involves uncertainty β in the input parameters, in the model structure, in the numerical approximations, and in the observation data used for validation. UQ provides a systematic framework for dealing with these uncertainties, moving from a single "best estimate" prediction to a probabilistic characterization that communicates what is known, what is uncertain, and how confident the prediction is. The field has its roots in statistics, probability theory, and numerical analysis, and has grown rapidly over the past two decades in response to the increasing use of computational models for high-stakes decisions.
UQ distinguishes two fundamental types of uncertainty. Aleatory uncertainty (also called irreducible or statistical uncertainty) arises from inherent randomness β the natural variability of earthquake magnitudes, ground motions, material properties, and structural responses. It cannot be reduced by better measurement or modeling; the only way to deal with aleatory uncertainty is to characterize its distribution. Epistemic uncertainty (also called reducible or model uncertainty) arises from lack of knowledge β imperfect models, incomplete data, uncertain parameters, and idealized assumptions. It can in principle be reduced by better measurement, modeling, or data, though in practice the reduction may be slow or expensive. UQ methods handle aleatory and epistemic uncertainty differently, and the distinction is important for decision-making: reducing epistemic uncertainty is a worthwhile investment, while reducing aleatory uncertainty is not possible.
UQ encompasses several core activities and methods. Forward propagation takes uncertainty in inputs and computes the resulting uncertainty in outputs β using methods such as Monte Carlo simulation, polynomial chaos expansion, and spectral methods. Inverse problems and Bayesian inference take observations and infer the probability distributions of model parameters β using methods such as Markov Chain Monte Carlo (MCMC), variational inference, and Bayesian neural networks. Sensitivity analysis identifies which inputs have the greatest influence on the output uncertainty β using methods such as variance-based sensitivity (Sobol indices), local sensitivity (derivatives), and screening methods (Morris). Model calibration adjusts model parameters to match observed data while accounting for uncertainty. Model validation assesses whether a model is adequate for its intended use, given the available data. Reliability analysis computes the probability of failure or of exceeding a performance threshold. In earthquake engineering, UQ is central to probabilistic seismic hazard analysis (PSHA), performance-based earthquake engineering (PBEE), and seismic risk assessment. Key challenges include: (1) the curse of dimensionality in high-dimensional input spaces; (2) the cost of running expensive simulations many times; (3) the difficulty of separating aleatory from epistemic uncertainty in practice; (4) the interpretation of probabilistic results for decision-making; and (5) the need to communicate uncertainty effectively to engineers, owners, and the public. Modern practice increasingly uses surrogate models to make UQ tractable, Bayesian methods to handle epistemic uncertainty rigorously, and visualization and communication tools to convey uncertain results. In Iran, UQ is increasingly used in seismic hazard studies, in performance-based design, and in research on structural reliability and risk assessment.