Structural health monitoring with accelerometers provides notable benefits over strain gauges, particularly in installation time and cost efficiency. However, effective local damage assessment necessitates access to local stress histories. This paper proposes a methodology that integrates two distinct approaches to identify and predict stress and strain across various bridge locations from sparse monitoring via acceleration data. The proposed model is validated using strain histories and accelerations collected from the composite railway Bryngeån Bridge in Sweden during its in-service conditions. Initially, a deep learning algorithm for sequence data is employed to forecast strain histories from acceleration data gathered across various bridge locations. Subsequently, the local response function method is implemented, utilizing experimental data collected from the bridge and employing localized models of its substructures, allowing predictions of the bridge's local strain. By integrating these methods, the approach enables accurate prediction of stress ranges and cycles for critical non-instrumented parts, minimizing the need for extensive direct instrumentation and providing a cost-effective, efficient solution for operational structural health monitoring.