Optical fiber shape sensing technology has gained widespread attention in the field of spatial shape perception due to its unique advantages. Strain sensing measurement, bending information computing, and shape reconstruction algorithms are key components of optical fiber shape sensing technology. The conventional numerical computation method for shape sensing is based on the geometric relationship of sensing fibers, which is cumbersome, and the accuracy of shape sensing may be influenced by various factors during the computation process. To avoid complex numerical calculations and potential errors, methods based on neural networks for shape sensing have become a research focus. However, current neural network methods have not established a direct mapping relationship between strain measurement results and fiber shape spatial coordinates, nor do they address the situation of distributed strain measurement. In this study, we propose a multi-core fiber shape coordinate prediction network model that integrates convolutional neural network-long short-term memory (CNN-LSTM) and an attention mechanism. This model effectively avoids complex numerical calculations and directly obtains shape coordinates from the distributed strains of the three cores in the multi-core fiber. A distributed strain measurement system based on optical frequency domain reflectometry (OFDR) technology is used to collect data and construct a dataset for network testing. The coordinate prediction and curve shape reconstruction results of the method proposed are compared and analyzed with numerical calculation methods, the LSTM network, and the CNN-LSTM network.

The input data of the proposed network model are the distributed strains of the three cores in a three-core optical fiber, and the output data are the spatial coordinates of the optical fiber. The input data are three-dimensional, and the output data are two-dimensional. The proposed network model includes a CNN module, an LSTM module, a Dropout layer, an attention mechanism layer, and two independent fully connected layers. The CNN module extracts features from the input data, with a batch normalization layer to normalize the data, a convolution layer to increase the feature dimension, and a pooling layer for max pooling. The LSTM module mines temporal features, with a dropout layer introduced to prevent overfitting. The temporal features are further processed by the attention mechanism to reduce the effect of secondary features. Two independent fully connected layers process the two-dimension outputs, with the output of each fully connected layer taking the value of the last time step in the sequence as the predicted value. The network training dataset is derived from the core strain and shape coordinate values obtained from a finite element model of multi-core optical fibers, while the testing dataset is constructed from actual measurement data from a distributed strain measurement system based on OFDR technology. We compare the distribution of the true and predicted horizontal and vertical coordinates corresponding to curves with two different curvature radii. Additionally, we conduct a comparative analysis of five scenarios: the original shape, numerical computation, prediction by the LSTM network, prediction by CNN-LSTM, and prediction by the proposed network model.

The comparison of curve coordinates shows that the true and predicted values of the curve coordinate with two different curvature radii have consistent distribution intervals (Fig. 6 and Fig. 7). The comparison of shape reconstruction results indicates that the curve shape predicted by numerical computation methods has a larger error compared to neural network-based predictions. The curve shape predicted by the proposed network model is closest to the original curve, maintaining good consistency even at the far end of the sensing fiber. The error reduction when using only the LSTM network, CNN-LSTM network, and the proposed network demonstrates that the designed model more accurately predicts curve shape coordinates. The CNN module, LSTM module, and attention mechanism all contribute significantly to improving the accuracy of coordinate prediction. For a curve with a curvature radius of 700 mm, the root mean square error (RMSE) is only 1.5739 mm, and the mean absolute error (MAE) is 0.6919 mm, which are 0.928 mm and 0.2224 mm higher than those of the numerical computation method, representing improvements of 58.96% and 32.14%, respectively. The error may stem from both the network model’s limitations and placement inaccuracies between the multi-core fibers and shape models during the experiment.

We propose a multi-core fiber shape coordinate prediction model based on CNN and LSTM networks, combined with an attention mechanism, to address the complex numerical computation challenges in optical fiber shape sensing. The model directly obtains shape coordinates from distributed strain data, thus achieving shape sensing. CNN and LSTM modules extract temporal features from strain data, while the attention mechanism suppresses secondary temporal features to improve the final shape coordinate predictions. Experimental results demonstrate that for curves with different curvature radii, the proposed method avoids complex numerical computation and achieves optical fiber shape sensing. The RMSE and MAE are both superior to those obtained using numerical computation based on the Frenet-Serret equation. For a curve with a curvature radius of 700 mm, the RMSE is only 1.5739 mm and the MAE is only 0.6919 mm, showing improvements of 58.96% and 32.14%, respectively, compared to numerical computation results. The proposed method has promising potential for application in optical fiber distributed strain measurement for shape sensing.