Resistivity-enhanced multi-physics machine learning framework for dynamic stress prediction in high sensitive UHPC

Accurate real-time monitoring of compressive stress in ultra-high performance concrete (UHPC) is critical for ensuring the safety and longevity of long-span bridges, super-tall buildings, and other complex structures. Traditional sensors, such as piezoelectric or fiber-optic devices, often suffer from durability limitations, high costs, and poor compatibility with concrete matrix deformation. Machine learning has emerged as a powerful tool for modeling UHPC’s nonlinear mechanical behavior, but existing models primarily rely on strain or displacement inputs, yielding limited accuracy.

Now, a team of researchers from University of Shanghai for Science and Technology has developed a machine learning framework that substantially improves dynamic stress prediction for HS-UHPC by integrating electrical resistivity as a complementary input parameter.

“Traditional stress prediction models miss a critical piece of information: how the material’s internal structure changes under load,” said Lin Chi, corresponding author of the paper, associate professor of the School of Environment and Architecture, University of Shanghai for Science and Technology. “Electrical resistivity captures those microstructural changes directly. When you combine that with displacement data, the machine learning model gains a much more complete picture of what is happening inside the concrete.”

The study, published in Lifeline Emergency and Safety on January 12, 2026, compared three machine learning algorithms—double-layer neural network (DLNN), boosting tree (BT), and squared exponential Gaussian process regression (SE-GPR)—using 446 experimental datasets from HS-UHPC under uniaxial loading. Two input configurations were tested: Dataset I containing mix proportions and displacement only, and Dataset II adding resistivity measurements.

Results showed that incorporating resistivity increased the coefficient of determination (R²) by 0.06 across models compared to displacement-only inputs. The SE-GPR model achieved the highest performance under dual-input conditions (R²=0.85, RMSE=0.11), with a 41.1% reduction in mean absolute error. The BT and DLNN models also benefited, with error reductions of 12.3% and 16.9%, respectively.

Sensitivity analysis revealed that displacement had the strongest individual correlation with compressive stress (coefficient=0.51), while resistivity showed a moderate positive correlation (coefficient=0.20). Importantly, the low correlation coefficient between resistivity and displacement (0.26) indicates high mutual independence, allowing them to serve as complementary variables that collectively enhance model accuracy while mitigating overfitting risks.

“What makes this approach particularly valuable for emergency and safety applications is its passive sensing capability,” added Lin Chi. “Because resistivity is an intrinsic material property, we can achieve high-precision stress monitoring without embedding external sensors that may fail over time. This is a fundamental shift toward self-sensing infrastructure.”

The research team notes that steel fiber and carbon nanotube (CNT) content, while weakly correlated with stress directly, play crucial roles in modulating electrical response. Steel fiber content showed a moderate positive correlation with resistivity (coefficient=0.30), while CNT concentration exhibited a strong inverse correlation (coefficient=–0.66). These upstream variables influence stress prediction indirectly through resistivity modulation, with steel fibers primarily modifying conduction pathways via crack-bridging effects and CNTs establishing percolation networks that distort under load.

Looking ahead, the team aims to extend the framework toward practical deployment. “Our next step is to validate this approach under real-world conditions, including varying temperature, humidity, and long-term cyclic loading,” said Chi. “We also plan to integrate the framework with wireless monitoring systems and explore its application to other cement-based materials. The ultimate goal is to develop a robust, low-cost, passive structural health monitoring system that can provide early warning of stress-induced damage in critical infrastructure—bridges, tunnels, and high-rise buildings—without relying on vulnerable embedded sensors.”

The work was supported by the Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering under Grant No. 2022B1212010016.

Other contributors include Chenlong Qiang, Rui Zhu, Shicheng Cui, and Lifei Zhang.