Deep neural networks predict seismic response of rocking rigid bodies in buildings

Every year, earthquakes claim most of their victims not through collapsing buildings but through what falls from shelves, desks, and laboratory benches. A hospital’s MRI machine, a data center’s server racks, a museum’s unanchored vase—each of these free-standing objects behaves, during strong shaking, like what engineers call a rocking rigid body: an object that pivots on its edges rather than flexing like a structure. Whether such an object topples over can mean the difference between an inconvenient cleanup and a lethal cascade of falling equipment. Now, a team of earthquake engineers from Beijing University of Civil Engineering and Architecture and the University of Science and Technology Beijing has developed a deep neural network capable of predicting, in a fraction of a second, whether a rigid body standing inside a building will overturn during an earthquake—achieving a reported accuracy of 94.37 percent on test data and dramatically outperforming the conventional machine learning methods that preceded it.

The work, published in Earthquake Engineering and Engineering Vibration, addresses a computational bottleneck that has long frustrated the seismic assessment of nonstructural components, the category that includes furniture, mechanical equipment, storage racks, and countless other objects whose failure during earthquakes is often more dangerous than damage to the buildings themselves. The problem is fundamentally one of scale and interaction. To predict whether a bookshelf on the fifth floor of a fifteen-story apartment building will topple, an engineer cannot simply analyze the bookshelf in isolation. The bookshelf sits atop a floor that amplifies and distorts the ground motion beneath the building. Floors high up in tall structures experience accelerations several times larger than those at ground level, and the character of that motion—its frequency content, its duration, its peaks—changes in ways that depend on both the building’s dynamic properties and the earthquake’s own signature.

The classical approach to this problem requires two nested analyses. First, engineers must perform a nonlinear time-history analysis of the entire building, feeding it a recorded or synthetic ground motion and computing how every floor responds second by second. Then, they must take the resulting floor motion and use it as input to a separate rocking-body dynamic analysis, tracking the object’s rotation angle as it pivots, impacts, and—if things go badly—tips past its critical angle. Each of these analyses is computationally demanding in its own right, and the rocking problem is notoriously ill-conditioned. Unlike linear structural systems, a rocking body’s response is extremely sensitive to tiny changes in initial conditions and input motion: two nearly identical earthquakes can produce wildly different outcomes for the same block, a chaotic quality that has made rocking motion famously difficult to predict since George Housner’s foundational work on inverted pendulum structures in 1963.

Compounding the difficulty, the interactions among the three governing factor families—seismic motion characteristics, structural amplification effects, and the geometric properties of the rocking body—are deeply nonlinear and resist the simple empirical equations that engineers have traditionally relied upon. A taller, slenderer block has a lower critical rocking angle and a longer characteristic rocking frequency; a squat block is more stable but slides more readily. Meanwhile, floor motions embed the amplified response of the building’s higher modes, and strong-motion duration influences how many rocking cycles an object experiences before shaking subsides. Capturing all of this with a formula has proven elusive.

The Chinese team’s solution is to sidestep the physics simulation entirely, at least at prediction time, by letting a deep neural network learn the mapping directly from data. The researchers began with city-scale nonlinear time-history analyses—the same simulation technology used to model how thousands of buildings across an entire urban area respond simultaneously to a scenario earthquake. From these analyses, they extracted the seismic responses at building floors, which then served as excitation for rocking-body dynamics calculations. For every combination of ground motion, building, and floor level, they computed the corresponding rocking response and recorded whether the body overturned. This process generated a multidimensional database spanning a wide range of ground-motion intensity measures, building heights, and rigid-body geometries.

Ground-motion intensity measures deserve a brief explanation, because they are the language in which engineers compress a complicated earthquake into a handful of numbers. Quantities such as peak ground acceleration, peak ground velocity, spectral accelerations at various periods, Arias intensity, and cumulative absolute velocity each summarize different aspects of a record—its amplitude, its energy content, its duration—and decades of research have explored which of these measures best correlates with damage of various kinds. For rocking bodies, the choice is particularly delicate, since overturning depends on a subtle interplay of all of these factors rather than on any single one. By incorporating a rich suite of intensity measures into the input features, the researchers gave their neural network access to the multiple dimensions along which earthquake danger manifests.

On top of this database, the team trained a deep neural network to perform what is essentially a binary classification task: given the intensity measures characterizing the ground motion, the height of the building, the floor level, and the geometric parameters of the rigid body, predict whether the object will overturn. Deep neural networks excel precisely where conventional regression struggles, because their layered architecture can represent highly nonlinear, high-dimensional relationships among inputs. Each layer of the network transforms its inputs through learned weights and nonlinear activation functions, allowing successive layers to build up increasingly abstract representations of the underlying physics—representations that no human analyst would need to specify by hand.

The results are striking. The trained model achieved 94.37 percent accuracy on its test set, exceeding the performance of conventional machine learning approaches such as random forests, support vector machines, and decision trees, which the authors used as benchmarks. Just as importantly for practical deployment, the network achieves high computational efficiency: once trained, it produces predictions essentially instantaneously, whereas a full coupled building-and-rocking-body analysis can take minutes to hours per case. For risk analysts who need to estimate, across an entire city, how many thousands of cabinets, servers, and shelves will topple in a given earthquake scenario, that difference is transformative.

The team also explored dimensionality reduction—mathematical techniques that compress the input feature space while discarding redundant information. Remarkably, reducing the number of input features decreased both training time and model complexity while preserving strong predictive performance. This finding matters for two reasons. Practically, it means the method can run on more modest computing resources and be more easily embedded in rapid assessment workflows. Scientifically, it suggests that a relatively small subset of intensity measures and geometric parameters captures most of the information relevant to overturning—a valuable insight for future fragility studies of building contents.

The work builds on a growing body of research applying artificial intelligence to seismic response prediction, and it arrives at a moment when the field of urban earthquake simulation is maturing rapidly. City-scale nonlinear time-history analysis, which underpins the new study’s training database, has itself only become feasible in recent years through advances in computational structural engineering, and it now serves as the engine for post-earthquake damage assessment systems that can estimate regional losses within hours of a real event. Extending that simulation capability to nonstructural contents through machine learning closes an important gap, because previous rapid assessment frameworks focused almost exclusively on the buildings themselves.

The implications extend well beyond furniture. Critical facilities—hospitals, power substations, semiconductor fabs, emergency operations centers—are filled with free-standing and lightly anchored equipment whose overturning can trigger system-level failures far costlier than any structural damage. Museum collections, cultural heritage artifacts, and laboratory chemicals represent other categories where rocking and overturning carry severe consequences. A rapid, accurate overturning prediction tool enables engineers to generate fragility curves—probabilistic statements about the likelihood of overturning as a function of shaking intensity—for entire inventories of contents, which in turn feeds into loss estimation, retrofit prioritization, and the design of protective measures such as anchoring, base isolation pads, and tie-down systems.

The study was supported by the National Natural Science Foundation of China and the Institute of Engineering Mechanics of the China Earthquake Administration, among other funders. Its authors—Qingle Cheng, Zhengxuan Song, Linlin Xie, and Yuan Tian—position the approach as an efficient and intelligent framework for the seismic assessment and risk analysis of rocking components in buildings, and the broader trajectory of the research suggests a future in which earthquake early warning systems, city-scale simulators, and machine learning predictors work in concert to warn not only about collapsing structures but about the contents inside them. In an era when most earthquake deaths in countries like Japan and the United States stem from nonstructural failures rather than structural collapse, an algorithm that can instantly flag which objects in which buildings are likely to topple may prove to be one of the more consequential applications of deep learning in the earthquake engineering toolbox.