Machine Learning and Bayesian Statistics Rebuild Earthquake Fragility Curves from Italy’s 1980 Irpinia Disaster

More than four decades after a magnitude 6.9 earthquake tore through Campania and Basilicata, killing nearly 2,500 people and leveling entire hilltop towns, the damage records of the 1980 Irpinia disaster are being put to work again. In a new study published in the Bulletin of Earthquake Engineering, Carlo Del Gaudio and Gerardo Mario Verderame of the University of Naples Federico II have combined machine learning with Bayesian statistics to extract some of the most detailed seismic fragility curves ever produced from a historical Italian damage database. Their framework does something prior studies could not: it fills in the gaps left by post-earthquake surveyors in 1980, and it treats the ground shaking estimates themselves as uncertain quantities rather than as fixed facts.

The starting point is the Da.D.O. platform, the Database of Observed Damage maintained by the Italian Department of Civil Protection and Eucentre. Across fifty years of Italian earthquakes, from Friuli in 1976 to Emilia in 2012, the platform now holds damage data for roughly 320,000 surveyed buildings, about 78 percent of them masonry structures and 8 percent reinforced concrete. For the Irpinia event specifically, the researchers drew on inspections carried out in forty-one municipalities in Southern Italy, chosen to span the full range of macroseismic intensities generated by the shock. The stock is dominated by masonry, particularly rubble stone and tuff, with reinforced concrete buildings a small minority, most of them built between 1960 and 1980 and designed for gravity loads alone, with no consideration of seismic forces.

But the archive has a serious flaw. Nearly 47 percent of the reinforced concrete buildings have no recorded construction age, more than double the missing fraction among masonry buildings. That gap matters because construction age is one of the strongest proxies for seismic vulnerability: it encodes the design code in force, the quality of materials, and the construction practices of the era. Rather than discarding nearly half the reinforced concrete inventory, the researchers trained a supervised machine-learning classifier to infer the missing ages from the attributes that inspectors did record, including vertical and horizontal structural systems, roof type, number of storeys, number of housing units, average floor area, municipality, and even observed damage.

The team compared a full arsenal of algorithms in MATLAB’s Classification Learner environment, including decision trees, support vector machines, logistic regression, k-nearest neighbors, naive Bayes classifiers, and neural networks. The best performer was an optimizable ensemble that achieved a cross-validated accuracy of 59.8 percent, automatically selecting a bagged ensemble of 449 classification trees from a set of ten predictors. Accuracy rose above 90 percent in area-under-curve terms for the two extreme building periods, pre-1900 and 1972 to 1980, while intermediate classes proved harder to separate, an expected result when structural features evolve gradually over time. Crucially, Shapley value analysis showed the classifier leaned on physically meaningful signals: the horizontal structural system was the most influential predictor, reflecting the historical shift from wooden and vaulted floors to reinforced concrete slabs, with vertical structure and municipality close behind. Damage variables had negligible influence, which reduces the risk of circular reasoning in the subsequent fragility analysis.

The second, arguably more consequential innovation concerns how the ground shaking itself is handled. Empirical fragility studies typically rely on ShakeMap-derived intensity measures, which blend ground-motion prediction equations with instrumental recordings. These products carry inherent uncertainty, and most studies simply ignore it. That omission produces a classic statistical pathology known as attenuation bias, or regression dilution: measurement error in the predictor variable gets absorbed into the response model, artificially inflating the dispersion of the estimated fragility curves. Del Gaudio and Verderame instead modeled ShakeMap uncertainty explicitly, treating the true intensity at each municipality as a latent variable drawn from a spatially correlated random field, with correlations between locations decaying with distance in the manner described by Jayaram and Baker.

Within a Bayesian framework, the researchers used Markov Chain Monte Carlo sampling, specifically the Metropolis-Hastings algorithm, to estimate the parameters of lognormal fragility functions, which describe the probability of exceeding a given damage state as a function of ground motion intensity. Twenty thousand iterations were run, with 3,000 discarded as burn-in, and prior distributions for the median and dispersion parameters were constructed from European and Italian fragility models, including the European Building Vulnerability Database, the Global Earthquake Model’s vulnerability model, and the European Seismic Risk Model ESRM20. The observed damage of each building entered the likelihood as a Bernoulli variable, and posterior samples captured uncertainty in both the fragility parameters and the latent intensity field simultaneously.

The results are striking. When intensity uncertainty was ignored, dispersion parameters ballooned to implausible values: 1.82 for reinforced concrete buildings at the first damage state, 2.14 for tuff masonry, 1.36 for brick, 1.46 for rubble. Once the latent intensity field was introduced, dispersions collapsed into a narrow band of roughly 0.6 to 0.8 across all typologies and damage states. In other words, much of the apparent scatter in historical damage data was never a property of the buildings at all; it was an artifact of treating interpolated shaking estimates as if they were certain. The corrected curves also show a cleaner, monotonic progression across damage states, with medians rising as severity increases and minimal overlap between thresholds, exactly what a physically credible fragility model should look like.

The refined taxonomy then delivers a detailed vulnerability hierarchy of the Irpinia building stock. Rubble stone masonry emerges as the most vulnerable typology, followed by tuff and then brick masonry, consistent with the irregular geometry and weak mechanical properties of rubble construction. Within each vertical typology, the horizontal system proves decisive: buildings with wooden floors or vaults consistently perform worse than those with steel or reinforced concrete diaphragms, and high-rise masonry buildings are generally more fragile than low-rise ones. Reinforced concrete buildings show their own pattern, with pre-1970 construction more vulnerable than later buildings and tall structures more fragile at low damage states. The authors suggest this taxonomy, which exploits every attribute in the original inspection forms rather than collapsing buildings into broad EMS-98 vulnerability classes, offers a template for future empirical fragility work.

Perhaps the most provocative finding concerns which ground motion descriptor best explains the observed damage. Comparing peak ground acceleration, peak ground velocity, and spectral acceleration at 0.3 seconds, the researchers evaluated efficiency in two independent ways: through the standard deviation of residuals in a probit representation of the damage data, and through Bayesian Information Criterion-based likelihood comparisons. Both methods converge on the same answer. Peak ground acceleration, long the default choice in seismic risk practice, generally performs the worst, showing the largest residual scatter. Peak ground velocity provides the strongest and most consistent explanatory power, especially for moderate-to-high damage states, a result the authors link to its closer connection with the kinetic energy imparted to structures and the deformation demands that govern severe damage. The agreement between two methodologically independent tests strengthens the case that velocity-based intensity measures deserve a larger role in regional empirical fragility assessment.

Finally, the team compared their Irpinia curves against fragility models derived from the 2009 L’Aquila earthquake, another Da.D.O. dataset from a very different building culture. The comparison reveals how much regional practice and the history of seismic classification matter. Most L’Aquila municipalities had been designated seismic since 1915, while many Irpinia towns were first classified only after 1980, so their reinforced concrete buildings differ fundamentally in design provenance. For tuff masonry, the correspondence is telling: buildings with wooden or steel slabs most resemble the bad-quality masonry classes defined in L’Aquila’s AeDES survey, while those with reinforced concrete slabs align with good-quality classes, and the match shifts with damage severity. Rubble masonry maps onto bad-quality classes, brick onto good-quality ones. The lesson is that fragility is not just a function of a structural label; it is woven from materials, floor systems, regulatory history, and even the survey forms used to describe them, and any national risk model that ignores that texture is smoothing away exactly the information that matters most.

Subject of Research: Empirical seismic fragility assessment of the Irpinia 1980 building stock using machine learning and Bayesian updating

Article Title: Bayesian updating of seismic fragility curves of the Irpinia 1980 building stock with machine-learning-supported data analysis

Article References: Del Gaudio, C., & Verderame, G. M. (2026). Bayesian updating of seismic fragility curves of the Irpinia 1980 building stock with machine-learning-supported data analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02669-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02669-5

Keywords: seismic fragility curves, Bayesian inference, machine learning, 1980 Irpinia earthquake, masonry buildings, reinforced concrete, ShakeMap, intensity measures, Markov Chain Monte Carlo, Da.D.O. database, vulnerability ranking, ground motion uncertainty