PSI - Issue 80

Dong Xiao et al. / Procedia Structural Integrity 80 (2026) 11–22 Dong Xiao et al. / Structural Integrity Procedia 00 (2023) 000–000

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(a) CNN model for impact localisation

Global Average Pool

Linear block

Input signal

Conv block 1

Conv block 2

Conv block 2

Dense block

Output location

Flatten

(b) CNN-LSTM model for impact force estimation

Input signal

Conv block 1

Conv block 1

Conv block 1

Output force

Linear block

LSTM

(c) TCN model for impact localisation and force estimation

Global Average Pool

Linear block

Output location

Flatten

Input signal

Residual TC block

Residual TC block

Residual TC block

Linear block

Output force

(d) Transformer for impact localisation and force estimation

Global Average Pool

Location Decoder

Output location

Input signals

Positional Encoding

Transformer Encoder

Conv block 1

Force Decoder

Output force

(e) GNN for impact localisation and force estimation

S2

S2

S1

S3

Output location/ force

S1

S3

Pool

Linear

S6

S4

S6

S4

S5

S5

Representation

Conv block 1

Conv block 2

Dense block

Linear

Dropout

Relu

Conv

Maxpool

Relu

Conv

BatchNorm Relu

Residual TC block

Linear block

Conv

Relu

Dropout

Conv

Linear

Dropout

Linear

Dropout

Relu

Conv

Fig. 1: Diagram of the deep learning architectures for impact identification.

The GNN model (Fig. 1(e)) extends its spatial modelling capabilities to dynamic force estimation. Here, each sensor is treated as a node, and graph-based message passing allows temporal features to propagate across the network. Time-varying node inputs are either encoded using temporal slices or processed through integrated temporal modules. The final output, either at the graph or node level, is decoded into the impact force sequence. The GNN’s structural inductive bias supports generalisation across varying sensor configurations and enhances resilience to environmental variability. In summary, each architecture o ff ers complementary strengths: CNN-LSTM and TCN excel in capturing fine grained and long-range temporal features; the Transformer leverages global attention mechanisms; and the GNN integrates spatial topology with temporal dynamics. Together, these models provide a diverse foundation for bench marking impact force estimation under diverse test conditions and environmental uncertainties.