Ship hull stress reconstruction with limited sensors: A time-domain coupled modal superposition method and parametric layout optimization

The growth in ship size and intelligence has raised the demands on structural health monitoring. This study addresses the challenge of improving stress reconstruction accuracy and engineering applicability under sensor-number constraints in structural health monitoring. A time-domain coupled modal superposition (TCMS) method is proposed, in which the estimation of modal coefficients is formulated as a joint time-domain problem with time-smoothing and other constraint equations. This reformulation decouples the number of participating modes from the number of measurement points, enabling richer use of modal data under sparse sensing and yielding more accurate stress reconstruction and more reliable fatigue assessment. In parallel, a priori sensor layout indicator S is developed based on the sensor–mode information matrix. The correlation between this quantitative indicator and time-domain reconstruction accuracy is systematically quantified. An optimized sensor layout selected solely based on S is further validated through numerical experiments, demonstrating higher reconstruction accuracy and an expanded spatial range of reliable reconstruction. Overall, the proposed TCMS method and S-based layout optimization strategy provide an integrated technical route that combines algorithmic enhancement with sensor layout design for full-field stress reconstruction of large ship structures under limited measurement points.