An inverse input–output method is proposed for long-term condition monitoring of civil infrastructures through monitoring the prediction error of air temperature recorded at the site of a structure. It is known that structural natural frequencies are affected by temperature. Hence, the proposed method considers the structural natural frequencies as input and temperature as output to train a machine learning algorithm (MLA). To this end, after signal preprocessing using the variational mode decomposition (VMD), different MLAs are employed, and the error associated with this prediction is regarded as damage–sensitive feature. It is hypothesised and further confirmed through solving numerical and benchmark problems that the prediction error deviates significantly from the upper bond control limit of an R-chart (errors signal) constructed based on the prediction error of temperature as soon as the damage occurs. The frequency–temperature scatter plots indicate a linear dependency between the natural frequencies and temperature. Moreover, the similar slope obtained for the regression line fitted to different frequency–temperature scatter plots indicates high collinearity among pairs of natural frequencies. This observation implies that an interaction term must be considered for such pairs of natural frequencies in the linear regression model. The results of both numerical and experimental studies further confirm that the interaction linear regression model is the most accurate machine learning algorithm for solving the inverse problem of predicting temperature using natural frequencies for condition monitoring of structures. The results of the proposed method are also compared with the direct strategy, whereby its superiority is demonstrated.

中文翻译：

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监测民用基础设施状态监测的现场温度预测误差

通过监测结构现场记录的气温预测误差，提出了一种用于民用基础设施长期状态监测的逆向输入输出方法。众所周知，结构固有频率受温度影响。因此，所提出的方法将结构固有频率作为输入，将温度作为输出来训练机器学习算法 (MLA)。为此，在使用变分模式分解 (VMD) 进行信号预处理后，采用不同的 MLA，并将与此预测相关的误差视为损伤敏感特征。假设并通过求解数值和基准问题进一步证实，一旦损伤发生，预测误差明显偏离基于温度预测误差构建的R图（误差信号）的键控上限。频率-温度散点图表明自然频率和温度之间存在线性相关性。此外，从拟合不同频率-温度散点图的回归线获得的相似斜率表明自然频率对之间存在高度共线性。这一观察表明，必须为线性回归模型中的此类自然频率对考虑相互作用项。数值和实验研究的结果进一步证实，相互作用线性回归模型是解决使用自然频率预测温度以进行结构状态监测的逆问题的最准确的机器学习算法。还将所提出方法的结果与直接策略进行了比较，从而证明了其优越性。