A real-time spatial deformation estimation method based on spatial curvature decomposition and interpolation

•The layout of strain sensors is more flexible and simpler.•The required parameters only include sensor coordinates and strain data.•Both static and dynamic deformations can be accurately estimated.•Both spatial and plane deformations can be measured. Structural deformation entails safety risks, and at times, direct measurement can be challenging, especially when reference points are unavailable. Therefore, the development of a practical and precise deformation estimation method is crucial. This paper introduces a strain-based method with spatial curvature decomposition and interpolation for estimating structural deformation. The proposed method was tested through numerical simulations of various static and dynamic deformation cases for different structures, including a railway track, a rigid hanger of a bridge under low-frequency dynamic loads, and a cantilever beam under high-frequency dynamic loads. The feasibility of the method was verified, and it was further validated by a field test on a railway track. Compared to existing strain-based methods, it offers more flexible sensor placement, requires fewer parameters, and can estimate dynamic, static, planar, and spatial deformations. This strain-based method shows promise for real-time structural deformation monitoring, enhancing safety assessments.