An adaptive multi-task learning method for response prediction and optimal sensor placement

Accurate and effective structural vibration response prediction is a fundamental yet challenging task in engineering. Despite extensive research endeavors, reliable multi-objective response prediction remains largely unexplored, which is due to two significant challenges: difficulties in sensor position selection and unbalanced response prediction across different tasks. To address these issues, an unbalanced sparse multi-task response prediction based on feature selection (USMuRFS) approach is proposed, which bridges the gap between predictive modeling and optimal sensor placement. Specifically, an adaptive multi-task prediction framework is designed, integrated with a sparsity-guided variable selection module to identify trustworthy sensors and multi-objective response prediction simultaneously. The innovative design of USMuRFS embodies two main aspects: first, USMuRFS incorporates an adaptive loss balancing module that encourages fair optimization of each sub-objective within the prediction tasks; second, a hybrid penalty is introduced to select sensors at the group-sparsity, individual-sparsity, and element-sparsity levels. These two components, i.e., the adaptive loss balancing module and sparsity regularized module, contribute to each other and constitute USMuRFS together. Experiments on synthetic datasets, standard aircraft models, and large commercial aircraft flight test datasets illustrate that USMuRFS distinctly outperforms previous approaches. This can provide reliable insights into optimal sensor placement in multi-task response prediction.