Temperature history reconstruction in steel box girders using limited data and proper orthogonal decomposition-based dimension reduction representation

•A framework using limited measurements and probabilistic methods for reconstructing temperature history is established.•A POD-based dimension reduction representation is proposed for generating high-frequency temperature components.•The reconstructed temperature history samples maintain the stochasticity of daily temperature variations. The monitoring temperature history of steel box girders inevitably contains gaps or anomalies due to the malfunctions of the structural health monitoring system. Traditional methods for reconstructing temperature histories face the challenge in accounting for the randomness of temperature variations caused by the uncertainty of complex environmental factors. This research proposes a framework for reconstructing the long-term temperature of steel box girders by combining the limited measurements with a proper orthogonal decomposition (POD) based dimension reduction representation approach, to account for the stochastic nature of daily temperature variations. Unlike the conventional Monte Carlo-based POD method, the developed POD-based dimension reduction representation approach effectively reduces the number of elementary random variables from thousands to two by introducing random functions serving as constraints, overcoming the challenge of high-dimensional random variables inherent in the Monte Carlo methods. The proposed approach divides the measured temperature histories into random high-frequency (HF) and deterministic low-frequency (LF) components and establishes the theoretical models of power spectral density and coherence functions of HF temperature components to accommodate the generation of HF temperature component samples, and finally reconstructs temperature samples by superimposing the LF components and generated HF component samples. The results from a practical example demonstrate that the statistical characteristics of representative HF temperature component samples generated by the POD-based dimension reduction representation align well with the corresponding targeted values, and the proposed method outperforms the traditional POD method, yielding a 60% efficiency enhancement without compromising computational accuracy. The developed framework owns apparent superiority in accuracy compared to the traditional POD and the long short-term memory methods, particularly in continuous and extensive missing data. Moreover, the reconstructed temperature samples with assigned probabilities present complete probabil