Stranded fiber optic cables are widely used in telecommunications, sensing, industrial monitoring, and other fields. The research on the three-dimensional shape reconstruction algorithm of stranded fiber optic cables is of great significance for cable maintenance, breakpoint positioning, building settlement monitoring, deformation sensing, etc. To obtain the shape and position information of optical cables, most of the current methods are based on manual calibration. Such methods are time-consuming, labor-intensive, inefficient, greatly affected by the cable laying environment, and difficult to implement, and the reconstruction result is rough. To solve the above problems, researchers have proposed corresponding solutions using different distributed strain measurement technologies combined with the "strain-deformation" model. However, these solutions are all based on the structure of multi-core parallel optical cables, and the original model is no longer applicable to the spiral structure of stranded fiber optic cables. Therefore, we propose a space curve reconstruction method based on stranded fiber optic cables. The strain along the optical cable is simulated, and the improved "strain-deformation" model makes it suitable for stranded fiber optic cables.

The space curve reconstruction method based on the stranded fiber optic cable proposed in this paper includes four processes. First, the model of the stranded fiber optic cable is simplified into a spiral structure, and the stranded fiber optic cable is generated on the software SOLIDWORKS with the space curve to be reconstructed as the central axis. In addition, the discrete strain values are simulated for the outer core of the optical cable according to the physical meaning of the strain. Second, the improved "strain-deformation" model is used to convert the discrete strain values into the curvature and torsion of the corresponding points on the curve. Third, the curvature and torsion of the curve are taken as the input values of the Frenet frame. The differential equation of Frenet is inversely solved, and the curve is reconstructed. The comparison of the coordinate error between the reconstructed curve and the real curve verifies that the proposed method is effective. Finally, some parameters in the model are adjusted, such as the sampling density of strain points, as well as the helix radius and the bending radius of the curve to be reconstructed, and the rule and scope of application of this method are discussed.

Researchers focus more on the optimization of the "strain-deformation" model to avoid the usage of expensive strain measurement means. According to the physical meaning of the strain and the software SOLIDWORKS, a strain simulation method is designed (Fig. 2). In addition, the "strain-deformation" model is improved according to the characteristics of the stranded fiber optic cable (Fig. 6), and the improved model accurately solves the direction angle and torsion of the curve (Fig. 7). Then, the curvature and torsion obtained are taken as the input of the Frenet frame to construct the curve, and the maximum curve reconstruction error is 2.1% (Fig. 8). The reconstruction effect of the same curve before and after the model improvement is compared to further reflect the superiority of the improved model. The maximum reconstruction error before the model improvement is 102%, while that after the model improvement is only 2.1%. This shows that the model before the improvement cannot be used for the curve reconstruction of the stranded fiber optic cable because it cannot accurately solve the torsion of the curve (Fig. 10). Finally, some parameters in the "strain-deformation" model are adjusted, and the factors affecting the reconstruction accuracy of this method are discussed (Figs. 11, 12, and 13). The experimental results shows that the most influential factor is the sampling density of strain points. When the strain point spacing changes from 10 mm to 20 mm, the reconstruction error will increase from 2.1% to 18.6%. The helix radius and the bending radius of the curve to be reconstructed have the least impact. When the variation of the helix radius is between 3 mm and 9 mm, the variation range of the maximum reconstruction error is 0.6%. When the bending radius of the curve changes between 50 mm and 400 mm, the variation range of the maximum reconstruction error is 0.75%.

In this paper, a space-curve reconstruction method based on stranded fiber optic cables is presented. The effectiveness of this method for space curve reconstruction is preliminarily verified by simulation. Then, the influence of some super parameters on the method is studied. The results show that the method is most affected by the sampling density of strain points but less affected by the helix radius and the bending radius of the curve. For a 300 mm-long stranded fiber optic cable, the best reconstruction effect can be achieved when it is equally divided into 30 sections, and the maximum reconstruction error is 2.1%. Compared with the existing shape reconstruction methods, the proposed method simulates the strain in the software SOLIDWORKS, which can make researchers focus more on the optimization of the curve reconstruction model and greatly reduce the cost of strain measurement means. Then, according to the characteristics of the stranded fiber optic cable, the "strain-deformation" model is improved so that the torsion of the curve is not affected by the spiral structure. Finally, on the basis of the proposed method, the factors that affect reconstruction accuracy are discussed. The applicability and robustness of the curve reconstruction method can be expanded with a higher sampling density of strain points.