Shanwu Li

Accurate prediction of the three-dimensional debris cloud state following hypervelocity impacts is critical for spacecraft shielding design, yet remains hindered by the extreme stochasticity of frag mentation and the computational trade-off between efficiency and the intractability of high-fidelity simulations. A primary challenge lies in the coupled prediction of multi-physical features, exhibiting complex, non-linear dependencies that traditional analytical methods and black-box surrogate models fail to capture simultaneously. To address this, we propose a Copula-Physics-Augmented Deep Neural Network (CPDNN) framework. By leveraging Copula theory to decouple marginal learning from dependency modeling and embedding physical constraints into a hierarchical architecture, CPDNN uniquely resolves the 3D structural complexity and multi-feature coupling inherent in debris cloud dynamics. Validated against extensive Smoothed Particle Hydrodynamics (SPH) simulations, the model achieves high-fidelity reconstruction of 3D morphologies and ensures physical consistency across coupled state variables, with scaling exponent similarities exceeding 0.99. Unlike conventional approaches, CPDNN demonstrates robust generalization in extrapolation regimes while maintaining computational efficiency. This work provides a robust, interpretable, and computationally efficient paradigm for modeling complex stochastic physical systems, offering a scalable pathway with the potential to accelerate the protection design and terminal ballistics assessment in complex impact scenarios.

The sensitivity limit of photogrammetry-based incoherent optical methods for full-field displacement measurements, achievable by the multi-pixel averaging method, has recently been theoretically established by deriving the Cramér–Rao lower bound (CRLB) on the variance of displacement estimators. However, it is essentially a loose lower bound due to the assumption of elementary rigid-body motion in the measurement model. In this study, we generalize the fundamental sensitivity limit model to dynamic flexible structures with spatially-varying deformation field, by explicitly integrating the modal superposition principle in deriving the CRLB. Specifically, a tight lower bound for the fundamental sensitivity limit model is quantitatively established, as δ_disp = σ_n/(2^B − 1) ·√r/√N_s, revealing its parametric dependence on the imaging noise level σ_n, the number of dominant modes r, the number of effective spatial pixels N_s, and the camera bit depth B. Notably, the sensitivity limit scales with √r, indicating that the achievable measurement sensitivity decreases with increasing modal complexity, a distinctive feature for a flexible structure that is absent in the rigid-body model. The derived model is validated through both numerical simulations and shake table lab experiments.

The sensitivity limit (minimum measurable displacement) of incoherent optical methods with digital cameras (e.g., photogrammetry with optical flow and digital image correlation) may be exceeded, according to recent studies, through an SVD-based adaptive spatial pixel averaging with natural dithering to overcome the quantization effect, enabling super-sensitivity fullfield displacement measurements. Particularly, it was found that the achievable sensitivity limit is constrained by the number of effective spatial pixels used for SVD-based weighted averaging; i.e., a large number of spatial pixels is typically required to achieve super sensitivity. Nevertheless, the spatio-temporal dynamics in this process is not fully understood and quantified. In this study, we theoretically quantify the roles of spatio-temporal samplings and derive the fundamental sensitivity limit of the SVD-based super-sensitivity photogrammetry method using the Cramér-Rao Lower Bound (CRLB) theory and the uncertainty propagation principle. Specifically, the equivalence between spatial and temporal samplings for the achievable super sensitivity of the SVD-based method is established; it implies that increasing either the number of spatial pixels or the number of temporal frames for the SVD-based weighted averaging equivalently improves the measurement sensitivity limit. Furthermore, the fundamental sensitivity limit of the SVD-based super-sensitivity photogrammetry method is theoretically derived, as the minimum measurable displacement is found to be δp∗ ∝ σ_n(1/ √ N_s + 1/ √ N_t), quantitatively dependent on the number of spatial pixels N_s and the number of temporal frames N_t for weighted averaging, and the noise level σ_n in the measurement system. Validations on the principle and derived model are conducted through numerical simulations and laboratory experiments. Overall, this work contributes to a rigorous general formula for the achievable sensitivity limit of the SVD-based super-sensitivity photogrammetry for full-field displacement measurements. In addition, the revealed quantitative spatio-temporal equivalence indicates that spatial and temporal samplings can compensate for each other to achieve super-sensitivity dynamic displacement measurements. Some remaining challenges and required future research are also discussed.

Interstory drift is a fundamental parameter in earthquake engineering to characterize damage states and performance levels of buildings. Defined as the relative displacement between adjacent floors, it is nearly impossible to measure directly in practice and must be derived from absolute displacement measurements. Among various displacement measurement techniques, photogrammetry has emerged as a prominent method for displacement and drift measurements owing to its full‐field, noncontact incoherent optical characteristics. However, the sensitivity of the existing photogrammetry method is significantly lower than required by precise drift measurements due to the following: (1) much smaller drift magnitudes than displacement itself, requiring higher measurement precision; and (2) quantization‐limited low sensitivity of photogrammetry, especially under large meters per pixel (MPP) conditions in field applications. In this work, we address quantitatively the challenge of precise interstory drift measurement under seismic excitation by exceeding the theoretical sensitivity limit inherent in photogrammetry. Specifically, we leverage the recent advances in breaking the theoretical measurement sensitivity limit in photogrammetry, and adapt a super‐sensitivity photogrammetry method for precise interstory drift measurements. Furthermore, we derive a mathematical model based on rigorous uncertainty propagation theory, for the first time, to quantify the achievable photogrammetry sensitivity for interstory drift, as ; it reveals not only the quantitative relation between the achievable interstory drift measurement sensitivity and that of the displacement , but also the parametric dependence on the key factors: the number of effective spatial pixels , the imaging noise level , the effective rank of the dominant modes , the digital camera bit depth B , and the MPP. Extensive numerical simulations and laboratory shake table tests on a building structure model under representative seismic excitation are conducted and discussed. The results indicate that the adopted method achieves super‐sensitivity interstory drift measurements, which even approach the performance of the coherent laser displacement sensors as the number of effective pixels increases; in addition, observations on the tests are found to be consistent, quantitatively, with the derived mathematical model. This work provides a quantitative super‐sensitivity photogrammetry method for interstory drift measurements.