A two-step scaled physics-informed neural network for non-destructive testing of hull rib damage

Nondestructive testing (NDT), a critical method for assessing the safety of ship structures, often requires large amounts of data. The physics-informed neural network (PINN), by integrating data with physical laws, offers an efficient approach to NDT, even when sampling data is limited. However, training PINNs often encounters challenges due to a mismatch between the gradients of the data loss and physical loss, a phenomenon known as gradient ill-conditioning. In this work, we propose a two step-scaled physics-informed neural network (TSS-PINN) to mitigate this issue, where both the variables within the neural network and those in the physical equations are scaled. Using one-dimensional hull ribs for illustration, the performance of TSS-PINN is compared with that of traditional PINN. While both methods effectively predict the distribution of elastic modulus along an ideal beam, only TSS-PINN can predict the elastic modulus distribution in hull ribs. Based on gradient analysis, we demonstrate that gradient pathology in PINNs varies with the positions. TSS-PINN can project boundary measurement points to central positions, thereby alleviating gradient ill-conditioning at the boundaries. Our findings indicate that TSS-PINN provides a simple and efficient approach to address unreasonable gradients in PINNs, especially in inverse problems such as NDT.