Encoder–decoder U-Net for damage severity prediction in laminated plates with continuous and discontinuous damage using derivative-enriched mode-shape images

This paper proposes a method for predicting damage severity in laminated composite plates by combining an improved mechanical model with physics informed deep learning. The main contribution of the study is the development of a new higher order shear deformation function based on an extension of Reddy’s function. The proposed function is intended to describe transverse shear effects more accurately and improve the accuracy of vibration characteristics. A parametric study is conducted to determine a suitable adjustment coefficient, allowing the model results to approach three dimensional elasticity solutions more closely. The reliability of the proposed formulation is evaluated by comparing the predicted vibration frequencies and corresponding responses with reference three dimensional solutions. Based on the validated mechanical model, mode shape images and their corresponding derivative fields are constructed within an isogeometric analysis framework. The inclusion of first order derivatives and the Laplacian helps highlight local variations in the vibration field caused by stiffness reduction in damaged regions. Four input configurations, M1 to M4, are established to separately assess the contribution of each feature group. Among them, M4 uses the complete set of 12 channels generated from the first three mode shapes and their corresponding derivative quantities. This mechanically informed dataset is then used as the input to an encoder-decoder U-Net architecture for predicting damage severity at the element level. The effectiveness of the proposed method is validated for both continuous and discontinuous damage regions. The robustness of the models is also examined under noise levels of 0%, 0.5%, 1%, and 2%. The results show that the configurations using derivative based features, particularly M3 and M4, achieve higher accuracy and better stability than the model using only mode shapes. M4 is able to accurately identify damage locations, reconstruct damage distributions, and quantify damage severity even when the damage pattern is complex or the input data contain noise. Incorporating mechanical information into the construction of the input dataset improves physical interpretability and increases the reliability of the deep learning model, indicating the potential of the proposed method for damage diagnosis and structural health monitoring of laminated composite structures.