Monitoring the vibration responses of structures accurately and efficiently is the key point of structural health monitoring (SHM). The monitoring of structural vibration responses depends on the sensor system. Therefore, discovering critical sensor positions is a challenging but beneficial task for SHM. Unfortunately, the predominant approaches only focus on predicting the vibration responses and lack the capability to identify meaningful sensor positions, which inevitably restricts their predictive capabilities. Furthermore, the strong linear correlation between sensors results in instability when selecting sensor locations, which leads to the difficulty of sensor optimization. To bridge this gap, we propose a sparse learning method with feature selection (SLMFS) to identify meaningful and interpretable sensor positions. In this method, to facilitate interpretation and stability, we use sparsity-inducing penalties to select the important sensors at both individual and group levels. In addition, we introduce independent regularization (IR) for stable and consistent feature selection. We also present an efficient iterative optimization algorithm to address the SLMFS, which is guaranteed to converge to the global optimum. The synthetic data, simulation data and laboratory data are used to validate the effectiveness and accuracy of SLMFS. The results show that sensor selection and response prediction mutually reinforce each other. On one hand, the guidance from sensors further ensures the response prediction produces a good representation. On the other hand, the good representation enables more precise selection of target response-related sensors. Therefore, our learning method could improve the efficiency and accuracy of response prediction

In aeronautical engineering, vibration response reconstruction is a critical yet challenging task. Despite some progress in recent years, existing methods still perform poorly due to a lack of consideration of effective sensor placement, especially when multiple responses need to be reconstructed simultaneously. In this article, we propose a cost-efficient and effective scheme, sparse parameter decomposition-adaptive response reconstruction (sdaRR) method, which performs optimal sensor placement while reconstructing the multitarget response. First, we propose a multitask learning module to reconstruct multiple responses simultaneously. We also meticulously design a simple yet effective adaptive weighting method to address the issue of reconstruction imbalance in multitask learning. Second, sparse regularization and parameter decomposition modules are introduced into the response reconstruction framework to precisely select the optimal sensors. Specifically, we explicitly separate the parameters into task-shared and task-specific regularization terms, which not only identify task-shared sensors but also task-specific sensors. This enhances the interpretability and reliability of multitarget response reconstruction, further improving accuracy. Extensive experiments conducted on both the standard aircraft and the large passenger aircraft models validate the effectiveness of our method. Compared with state-of-the-art methods, it demonstrates more robust reconstruction performance while maintaining strong interpretability. This can provide reliable insights into optimal sensor placement in response reconstruction.