A flexible curved surface shape reconstruction method based on neural network

Abstract

The application discloses a flexible curved surface shape reconstruction method based on a neural network, and comprises the following steps: collecting initial wavelength data and measured wavelength data of a distributed optical fiber sensor when a flexible substrate is respectively in a planar state and attached to a calibration curved surface provided by a calibration element, so as to calculate measured wavelength drift data or measured strain distribution data, and meanwhile, calculating measured three-dimensional coordinate data according to geometric parameters of the calibration curved surface, so as to train a selected neural network model; collecting current wavelength data of the distributed optical fiber sensor when the flexible substrate is attached to a target element to be measured, so as to calculate current wavelength drift data or current strain distribution data, and performing inference on the trained neural network model, so as to obtain predicted three-dimensional coordinate data. When the neural network is trained, the three-dimensional coordinate value information of the flexible substrate can be accurately obtained only through the calibration curved surface and a software algorithm, so that the cost is significantly reduced, and the environmental adaptability and reconstruction precision are improved.

Description

Technical Field

[0001] This invention relates to distributed optical fiber measurement technology, and more particularly to a method for reconstructing the shape of flexible curved surfaces based on neural networks. Background Technology

[0002] Flexible substrates play an increasingly important role in modern engineering, medicine, aerospace, and many other fields. They typically possess high deformability and adaptability, enabling them to respond to external stimuli under varying environmental conditions. This allows for their widespread application in various sensors, robots, smart wearable devices, and medical devices. With technological advancements, flexible substrates can not only adapt to complex shape changes but also provide real-time monitoring and feedback of deformation and stress distribution, becoming a crucial component of innovative technologies in many fields.

[0003] For example, in the medical field, flexible substrates are widely used in biosensors, flexible electronic devices, and wearable devices to monitor human health in real time, such as physiological parameters like blood pressure, heart rate, and body temperature. In the robotics field, flexible substrates are often used in soft robots and sensor arrays, which can dynamically adjust their shape according to changes in the external physical environment, thereby achieving more flexible operation and perception. In the aerospace field, flexible substrates are used in the external structure of aircraft and sensor arrays to help achieve real-time monitoring of the surface condition of aircraft.

[0004] In existing technologies, there are solutions for monitoring the deformation of flexible bodies based on the combination of fiber optic sensing and neural networks. For example, patent document CN119578216A discloses a kinematic modeling method for a soft robotic arm based on a convolutional neural network. This method uses a fiber Bragg grating sensor to detect the curvature and curvature deflection angle of the soft robotic arm, and then inputs the curvature and curvature deflection angle into a trained convolutional neural network to obtain the spatial position predicted by the convolutional neural network. However, this method requires the acquisition of the three-dimensional position information of reflective markers on the soft robotic arm through a vision sensor as training data when training the convolutional neural network.

[0005] However, the aforementioned existing technologies have obvious drawbacks: 1. The acquisition of three-dimensional position coordinate information relies on a visual sensor with high-precision motion capture function. This visual sensor, also known as a motion capture camera, is an expensive optical device with high hardware costs and complex system, making it difficult to promote and apply on a large scale. 2. Visual coordinate calibration is easily affected by occlusion, lighting and space limitations, and has very high requirements for the calibration environment. It cannot be used in environments without visual pathways, such as enclosed, dark, narrow or underwater environments, thus limiting its applicable scenarios. 3. The number of reflective markers is limited and the coordinate acquisition is sparse, making it difficult to meet the requirements of full-area high-precision reconstruction of large-area flexible substrates. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a flexible surface shape reconstruction method based on neural networks. By calibrating the surface and using software algorithms during neural network training, the three-dimensional coordinate information of the flexible substrate can be accurately obtained, significantly reducing costs and improving environmental adaptability and reconstruction accuracy.

[0007] The technical problem to be solved by the present invention is achieved through the following technical solution: A method for reconstructing the shape of a flexible curved surface based on a neural network includes the following steps: Step 1: Encapsulate the distributed fiber optic sensor in an orthogonal grid pattern within a flexible substrate; Step 2: When the flexible substrate is in a planar state, the initial wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system; Step 3: When the flexible substrate is attached to the calibration surface provided by the calibration element, the measured wavelength data of the distributed optical fiber sensor is acquired by the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. At the same time, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated according to the geometric parameters of the calibration surface. Step 4: Using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data, train the selected neural network model to obtain a trained neural network model. Step 5: When the flexible substrate is attached to the target element under test, the current wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system, and the current wavelength drift data or current strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. Step 6: Input the current wavelength drift data or current strain distribution data into the trained neural network model for inference, and receive the predicted three-dimensional coordinate data output by the neural network model.

[0008] Furthermore, the distributed optical fiber sensor includes a first optical fiber and a second optical fiber. The first optical fiber is bent to form multiple first sensing segments and multiple first connecting segments. Each first sensing segment is parallel to the length direction and arranged sequentially along the width direction. Each first connecting segment is connected between two adjacent first sensing segments. The second optical fiber is bent to form multiple second sensing segments and multiple second connecting segments. Each second sensing segment is parallel to the width direction and arranged sequentially along the length direction. Each second connecting segment is connected between two adjacent second sensing segments. The first sensing segments and the second sensing segments are stacked along the thickness direction to form an orthogonal grid structure.

[0009] Furthermore, in step 1, the process of encapsulating the distributed optical fiber sensor within the flexible substrate in an orthogonal grid configuration is as follows: Step 11: Cast and cure a flexible substrate in a flat mold to form a flexible underlayer; Step 12: Lay the first optical fiber flat on the surface of the flexible substrate, and bend the first optical fiber to form multiple first sensing segments and first connecting segments; Step 13: The flexible substrate is cast and cured in the flat mold, on the flexible bottom layer and the first optical fiber to form a flexible intermediate layer; Step 14: Lay the second optical fiber flat on the surface of the flexible intermediate layer, and bend the second optical fiber to form multiple second sensing segments and second connecting segments; Step 15: The flexible substrate is cast and cured in the flat mold, onto the flexible intermediate layer and the second optical fiber, to form a flexible top layer; Step 16: Demold the flexible bottom layer, flexible middle layer and flexible top layer to obtain a flexible substrate encapsulating the distributed optical fiber sensor.

[0010] Furthermore, in step 3, the measured wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated in combination with the initial wavelength data. Simultaneously, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated based on the geometric parameters of the calibration surface, as follows: Step 31: Attach the flexible substrate to the calibration surface and adjust the relative position between the flexible substrate and the calibration surface so that the calibration surface is in its initial orientation; Step 32: The distributed optical fiber sensor acquires the measured wavelength data of the calibration surface when it is in the initial orientation through the signal demodulation system, and calculates the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface in combination with the initial wavelength data. At the same time, the three-dimensional coordinate data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface is calculated according to the geometric parameters of the calibration surface. Step 33: Rotate the calibration surface around its own central normal to other positions according to the preset step rotation angle, so that the flexible substrate deforms as the calibration surface rotates; Step 34: The distributed optical fiber sensor acquires measured wavelength data when the calibration surface is in other orientations using the signal demodulation system, and calculates measured wavelength drift data or measured strain distribution data when the distributed optical fiber sensor is in other orientations using the initial wavelength data. At the same time, the measured three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in other orientations is calculated based on the rotation matrix. Step 35: Repeat steps 33-34 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration surface is in different orientations, as well as the measured three-dimensional coordinate data, are collected. Step 36: Repeat steps 31 and 35 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration elements are in different orientations, as well as the measured three-dimensional coordinate data, are obtained.

[0011] Furthermore, the calibration surface is a standard cylindrical surface. When the calibration surface is in the initial orientation, the center of the calibration surface is aligned with the center of the flexible substrate. The cylindrical arc length direction of the calibration surface is parallel to the length direction of the flexible substrate, and the cylindrical central axis direction of the calibration surface is parallel to the width direction of the flexible substrate. In step 33, when calculating the three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in the initial orientation, the length direction, width direction, and thickness direction of the flexible substrate when it is in a planar state are used as the X-axis direction, Y-axis direction, and Z-axis direction, respectively, to establish a three-dimensional spatial coordinate system. Based on the cylindrical surface parameter equation of the calibration surface, the measured three-dimensional coordinate values ​​of each sensing point in the three-dimensional coordinate system are calculated.

[0012] Furthermore, the geometric parameters of the calibration surface include the cylinder radius. The cylinder diameter, central axis, and central normal of the calibration surface when it is in the initial orientation are respectively used as the X-axis, Y-axis, and Z-axis of the three-dimensional spatial coordinate system. According to the cylindrical surface parameter equation of the calibration surface, the measured three-dimensional coordinate values ​​of the i-th sensing point when the calibration surface is in the initial orientation are as follows: in, Let the radius of the cylinder be the calibration surface. Let be the central angle parameter of the i-th sensing point in the parametric equation of the cylindrical surface. Let be the axis parameter of the i-th sensing point in the parametric equation of the cylindrical surface.

[0013] Furthermore, the rotation matrix of the calibration surface when rotated to the j-th orientation is as follows: in, The step rotation angle is... Let be the rotation angle between the j-th orientation and the initial orientation.

[0014] The measured three-dimensional coordinates of the i-th sensing point when the calibration surface is rotated to the j-th orientation are shown below: in, The measured three-dimensional coordinates of the i-th sensing point when it is in the initial orientation on the calibration surface.

[0015] Furthermore, there are multiple calibration elements, and the calibration surfaces of different calibration elements have different geometric parameters; after step 35, the following steps are also included: Step 36: Repeat steps 31 and 35 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration elements are in different orientations, as well as the measured three-dimensional coordinate data, are obtained.

[0016] Furthermore, each sensing point forms an array of sensing points arranged in m rows and n columns, where m and n ≥ 2; the measured wavelength drift data includes multiple measured wavelength drift matrices of the distributed optical fiber sensor, each measured wavelength drift matrix corresponding to a combination of conditions between the calibration surface and the orientation, and is composed of the measured wavelength drift of each sensing point under this combination of conditions according to the arrangement of the sensing point array; wherein, the measured wavelength drift matrix corresponding to the k-th calibration surface being in the j-th orientation in the measured wavelength drift data is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the measured wavelength shift of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation. Similarly, the measured stress distribution data includes multiple measured stress distribution matrices of the distributed fiber optic sensor. Each measured stress distribution matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured strain of each sensing point under this combination of conditions arranged according to the sensor point array. The measured stress distribution matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the measured strain at the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation. The measured three-dimensional coordinate data includes multiple measured three-dimensional coordinate matrices of the distributed optical fiber sensor. Each measured three-dimensional coordinate matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured three-dimensional coordinate values ​​of each sensing point under this combination of conditions, arranged according to the sensing point array. The measured three-dimensional coordinate matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This indicates the measured three-dimensional coordinates of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation.

[0017] Furthermore, the neural network model is a GA-BP neural network; in step 4, the steps for training the selected neural network model using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data are as follows: Step 41: Divide the measured wavelength drift data or measured strain distribution data into training dataset, verification dataset and test dataset according to the corresponding combined working conditions. Each combined working condition data includes all measured wavelength drift data or measured strain distribution data collected under the same combined working condition and its corresponding measured three-dimensional coordinate data. The same combined working condition data is only divided into one of the training dataset, verification dataset and test dataset. Step 42: Using the training dataset, iteratively optimize the GA-BP neural network based on the genetic algorithm to obtain the optimized initial parameters of the GA-BP neural network, and set the network weights and thresholds of the GA-BP neural network based on the optimized initial parameters; Step 43: Using the training dataset, update the network weights and thresholds of the GA-BP neural network layer by layer based on the backpropagation algorithm. During the training process, use the validation dataset to optimize the hyperparameters and judge the fitting effect of the GA-BP neural network. Finally, use the test dataset to test the actual performance and generalization ability of the trained GA-BP neural network to complete the training of the GA-BP neural network.

[0018] The present invention has the following beneficial effects: Based on parametric modeling and spatial rotation coordinate transformation, the present invention can accurately obtain the measured three-dimensional coordinate data of the distributed optical fiber sensor through only the calibration surface and software algorithm. Combined with the wavelength drift data or strain distribution data of the distributed optical fiber sensor, the neural network model is trained, realizing efficient and low-cost construction of training data for the neural network. No expensive coordinate calibration equipment is required, which can significantly reduce costs, improve environmental adaptability and reconstruction accuracy. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the steps of the flexible curved surface shape reconstruction method provided by this invention.

[0020] Figure 2 The flowchart illustrates the steps of step 1 in the flexible surface shape reconstruction method provided by this invention.

[0021] Figure 3 The flowchart illustrates the steps of step 3 in the flexible surface shape reconstruction method provided by this invention.

[0022] Figure 4 The flowchart shows the steps of step 4 in the flexible surface shape reconstruction method provided by the present invention.

[0023] Figure 5 This is an exploded view of the flexible substrate provided by the present invention.

[0024] Figure 6 This is a schematic diagram showing the bonding between the flexible substrate and the calibration element provided by the present invention.

[0025] Figure 7 A schematic diagram of the three-dimensional coordinates of each sensing point in the distributed optical fiber sensor provided by the present invention.

[0026] Figure 8 This is a schematic diagram of the network architecture of the GA-BP neural network provided by the present invention. Detailed Implementation

[0027] The present invention will now be described in detail with reference to the accompanying drawings and embodiments, examples of which are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0028] In the description of this invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0029] Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first," "second," or "third" may explicitly or implicitly include one or more of that feature. In the description of this invention, "multiple" means two or more, unless otherwise explicitly specified.

[0030] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," and "setting," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0031] Example 1 like Figure 1 As shown, a method for reconstructing the shape of a flexible curved surface based on a neural network includes the following steps: Step 1: Encapsulate the distributed fiber optic sensor in an orthogonal grid pattern within a flexible substrate.

[0032] In step 1, such as Figure 5As shown, the flexible substrate has a length direction, a width direction, and a thickness direction, and the length direction, width direction, and thickness direction are perpendicular to each other. The distributed optical fiber sensor includes a first optical fiber and a second optical fiber. The first optical fiber is bent to form multiple first sensing segments and multiple first connecting segments. Each first sensing segment is parallel to the length direction and arranged sequentially along the width direction. Each first connecting segment connects two adjacent first sensing segments. The second optical fiber is bent to form multiple second sensing segments and multiple second connecting segments. Each second sensing segment is parallel to the width direction and arranged sequentially along the length direction. Each second connecting segment connects two adjacent second sensing segments. The first sensing segments and the second sensing segments are stacked along the thickness direction to form an orthogonal grid structure.

[0033] Preferably, the width spacing of each first sensing segment along the width direction is the same, and the length spacing of each second sensing segment along the length direction is the same; most preferably, the width spacing and the length spacing are also the same.

[0034] like Figure 2 As shown, in step 1, the steps of encapsulating the distributed optical fiber sensor in an orthogonal grid manner within the flexible substrate are as follows: Step 11: Use a flexible substrate to cast and cure in a flat mold to form a flexible bottom layer.

[0035] Step 12: Lay the first optical fiber flat on the surface of the flexible substrate, and bend the first optical fiber to form multiple first sensing segments and first connecting segments.

[0036] In step 12, at least one end of the first optical fiber needs to extend outside the flat mold to connect with the signal demodulation system during sensing. Preferably, adhesive is used to pre-fix the beginning and end ends of each first sensing segment to the flexible substrate to prevent positional displacement of the first sensing segments.

[0037] Step 13: The flexible substrate is cast and cured in the flat mold, on the flexible bottom layer and the first optical fiber to form a flexible intermediate layer.

[0038] Step 14: Lay the second optical fiber flat on the surface of the flexible intermediate layer, and bend the second optical fiber to form a plurality of second sensing segments and second connecting segments.

[0039] In step 14, at least one end of the second optical fiber needs to extend outside the flat mold to connect with the signal demodulation system during sensing. Preferably, the adhesive is used to pre-fix the beginning and end ends of each second sensing segment to the flexible intermediate layer to prevent positional displacement of the second sensing segments.

[0040] Step 15: The flexible substrate is cast and cured in the flat mold, on the flexible intermediate layer and the second optical fiber to form a flexible top layer.

[0041] Step 16: Demold the flexible bottom layer, flexible middle layer and flexible top layer to obtain a flexible substrate encapsulating the distributed optical fiber sensor.

[0042] The flexible substrate can be, but is not limited to, a polymer material that is flexible after curing, such as silicone, polydimethylsiloxane, polyurethane elastomer, or hydrogel, and is cured at room temperature to avoid excessive shrinkage stress during high-temperature curing. The adhesive is preferably made of the same polymer material as the flexible substrate to avoid inconsistencies in their shrinkage rates.

[0043] Step 2: When the flexible substrate is in a planar state, the initial wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system.

[0044] In step 2, the distributed optical fiber sensor has multiple sensing points, which are cascaded along the first and second sensing segments to form an array of sensing points arranged in m rows and n columns along the length and width directions, where m and n ≥ 2; the initial wavelength data includes the initial center wavelength of each sensing point.

[0045] The distributed optical fiber sensor can use Rayleigh scattering points formed by the Rayleigh scattering effect of the optical fiber itself as the sensing points, or it can use wavelength division multiplexing gratings, identical weak gratings or weak reflection points pre-prepared in the optical fiber as the sensing points.

[0046] The wavelength division multiplexing grating refers to the fact that the fiber gratings in the distributed optical fiber sensor have different initial center wavelengths; the identical weak grating refers to the fact that the fiber gratings in the distributed optical fiber sensor have the same initial center wavelength.

[0047] When acquiring the initial wavelength data, the first and second optical fibers of the distributed optical fiber sensor are first connected to different single-channel signal demodulation systems, or connected to the same multi-channel signal demodulation system. When the flexible substrate is in a planar state, the signal demodulation system emits probe beams into the first and second optical fibers respectively, and then receives the reflected beams formed by the probe beams reflected by each sensing point in the first and second optical fibers. The system then performs wavelength analysis on the reflected beams of each sensing point to obtain the initial center wavelength of each sensing point.

[0048] When the distributed fiber optic sensor uses wavelength division multiplexing (WDM) gratings as sensing points, different WDM gratings, due to their different initial center wavelengths, can selectively reflect different bands in the probe beam. Therefore, the sensing signals of different sensing points can be distinguished by the wavelength of the reflected beam. Hence, the signal demodulation system used is a wavelength division multiplexing (WDM) system. When the distributed fiber optic sensor uses Rayleigh scattering points, identical weak gratings, or weak reflection points as sensing points, the reflection of the probe beam by the Rayleigh scattering points or weak reflection points is not wavelength selective. Although the reflection of the probe beam by the identical weak gratings is wavelength selective, different identical weak gratings, due to having the same initial center wavelength, can only selectively reflect the same band in the probe beam. Therefore, the sensing signals of different sensing points cannot be distinguished by the wavelength of the reflected beam. Hence, the signal demodulation system used is an optical frequency domain reflectance (OFDR) system.

[0049] Step 3: When the flexible substrate is attached to the calibration surface provided by the calibration element, the measured wavelength data of the distributed optical fiber sensor is acquired by the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. At the same time, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated according to the geometric parameters of the calibration surface.

[0050] In step 3, the calibration surface is a standard surface with known geometric parameters, including but not limited to standard cylindrical surfaces, standard conical surfaces, standard frustum surfaces, standard airfoil surfaces, and other regular or custom calibration surfaces, such as saddle surfaces.

[0051] By collecting wavelength drift data or strain distribution data from the distributed fiber optic sensor on different types of calibration surfaces, the neural network can learn various primitive curvature features, thereby generalizing and reconstructing arbitrarily complex surfaces in practical applications.

[0052] The measured wavelength drift data includes the measured wavelength drift of each sensing point, and the measured strain distribution data includes the measured strain of each sensing point; wherein, the measured strain of each sensing point is calculated based on the measured wavelength drift of the sensing point itself, combined with the relationship function between the wavelength drift and the strain.

[0053] The relationship between wavelength shift and dependent variable is shown in the following function: in, The strain of the sensing point, The wavelength shift of the sensing point. The initial center wavelength of the sensing point is... is the effective elastic-optical coefficient of the optical fiber.

[0054] When the distributed optical fiber sensor uses a wavelength division multiplexing grating as the sensing point, it is preferable to use the measured wavelength drift data to train the neural network model. In this case, it is not necessary to convert the measured wavelength drift data into the measured strain distribution data through the above-mentioned relational function in step 3. When the distributed optical fiber sensor uses a Rayleigh scattering point, an identical weak grating, or a weak reflection point as the sensing point, it is preferable to use the measured strain distribution data to train the neural network model. In this case, it is necessary to convert the measured wavelength drift data into the measured strain distribution data through the above-mentioned relational function in step 3.

[0055] Specifically, such as Figure 3 and 7 As shown, in step 3, the measured wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. Simultaneously, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated based on the geometric parameters of the calibration surface, as follows: Step 31: Attach the flexible substrate to the calibration surface and adjust the relative position between the flexible substrate and the calibration surface so that the calibration surface is in its initial orientation.

[0056] In step 31, the flexible substrate is attached to the calibration surface, which means that the flexible substrate is in close contact with the calibration surface provided by the calibration surface under its own weight or external pressure, but the two are not fixed to each other by glue or other means.

[0057] Step 32: The distributed optical fiber sensor acquires the measured wavelength data of the calibration surface when it is in the initial orientation through the signal demodulation system, and calculates the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface in combination with the initial wavelength data. At the same time, the three-dimensional coordinate data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface is calculated according to the geometric parameters of the calibration surface.

[0058] In step 32, the measured wavelength data includes the measured center wavelength of each sensing point, and the measured three-dimensional coordinate data includes the measured three-dimensional coordinate values ​​of each sensing point. After bonding, the flexible substrate deforms from a planar state to a curved state that matches the calibration surface of the calibration surface, causing the measured wavelength data and measured three-dimensional coordinate data of the distributed optical fiber sensor to change synchronously.

[0059] The i-th sensing point is located at the initial orientation on the calibration surface. The measured wavelength shift at that time is shown below: in, The i-th sensing point is positioned on the calibration surface. The measured center wavelength at that time The initial center wavelength of the i-th sensing point is when the flexible substrate is in a planar state.

[0060] The i-th sensing point is located on the calibration surface. The measured strain at that time is shown below: in, is the effective elastic-optical coefficient of the optical fiber.

[0061] In this embodiment, the calibration surface is a standard cylindrical surface, and its geometric parameters include the cylinder radius. When the calibration surface is in the initial orientation, the center of the calibration surface is aligned with the center of the flexible substrate, the arc length direction of the cylinder of the calibration surface is parallel to the length direction of the flexible substrate, and the central axis direction of the cylinder of the calibration surface is parallel to the width direction of the flexible substrate. When calculating the three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in the initial orientation, the length direction, width direction, and thickness direction of the flexible substrate when it is in a planar state are used as the X-axis direction, Y-axis direction, and Z-axis direction, respectively, to establish a three-dimensional spatial coordinate system. Based on the cylindrical surface parameter equation of the calibration surface, the measured three-dimensional coordinate values ​​of each sensing point in the three-dimensional coordinate system are calculated.

[0062] To simplify coordinate calculations, the preferred method is as follows: Figure 7 As shown, with the cylinder diameter, central axis, and central normal of the calibration surface in the initial orientation as the X-axis, Y-axis, and Z-axis of the three-dimensional spatial coordinate system, respectively, the measured three-dimensional coordinate values ​​of the i-th sensing point when the calibration surface is in the initial orientation, according to the cylindrical surface parametric equation of the calibration surface, are as follows: in, Let the radius of the cylinder be the calibration surface. Let be the central angle parameter of the i-th sensing point in the parametric equation of the cylindrical surface. Let be the axis parameter of the i-th sensing point in the parametric equation of the cylindrical surface.

[0063] Step 33: Rotate the calibration surface around its own central normal to other positions according to the preset step rotation angle, so that the flexible substrate deforms as the calibration surface rotates.

[0064] In step 33, when the calibration surface rotates, the relative angle between the flexible substrate and the calibration surface will change. As long as the calibration surface is not a standard sphere, the flexible substrate can deform under the rotation of the calibration surface, causing the measured wavelength data and measured three-dimensional coordinate data of the distributed optical fiber sensor to change synchronously.

[0065] Step 34: Acquire the measured wavelength data of the distributed optical fiber sensor when the calibration surface is in other orientations through the signal demodulation system, and calculate the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration surface is in other orientations by combining the initial wavelength data. At the same time, calculate the measured three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in other orientations according to the rotation matrix.

[0066] In step 34, the measured wavelength shift of the i-th sensing point when the calibration surface is in the j-th orientation is as follows: in, The i-th sensing point is positioned on the calibration surface. The measured center wavelength at that time The initial center wavelength of the i-th sensing point is when the flexible substrate is in a planar state.

[0067] The i-th sensing point is located on the calibration surface. The measured strain at that time is shown below: in, is the effective elastic-optical coefficient of the optical fiber.

[0068] The rotation matrix of the calibration surface when rotated to the j-th orientation is shown below: in, The step rotation angle is... Let be the rotation angle between the j-th orientation and the initial orientation.

[0069] The measured three-dimensional coordinates of the i-th sensing point when the calibration surface is rotated to the j-th orientation are shown below: in, The measured three-dimensional coordinates of the i-th sensing point when it is in the initial orientation on the calibration surface.

[0070] Step 35: Repeat steps 33-34 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration surface is in different orientations, as well as the measured three-dimensional coordinate data, are collected.

[0071] Preferably, there are multiple calibration elements, and the calibration surfaces of different calibration elements have different geometric parameters; after step 35, the following steps are also included: Step 36: Repeat steps 31 and 35 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration elements are in different orientations, as well as the measured three-dimensional coordinate data, are obtained.

[0072] Step 4: Using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data, train the selected neural network model to obtain a trained neural network model.

[0073] In step 4, the measured wavelength drift data includes multiple measured wavelength drift matrices of the distributed optical fiber sensor. Each measured stress distribution matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured wavelength drift of each sensing point under this combination of conditions according to the sensor point array arrangement. The measured wavelength drift matrix corresponding to the k-th calibration surface being in the j-th orientation in the measured wavelength drift data is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This indicates the measured wavelength shift of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation.

[0074] Similarly, the measured stress distribution data includes multiple measured stress distribution matrices of the distributed fiber optic sensor. Each measured stress distribution matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured strain of each sensing point under this combination of conditions arranged according to the sensor point array. The measured stress distribution matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the measured strain at the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation.

[0075] The measured three-dimensional coordinate data includes multiple measured three-dimensional coordinate matrices of the distributed optical fiber sensor. Each measured three-dimensional coordinate matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured three-dimensional coordinate values ​​of each sensing point under this combination of conditions, arranged according to the sensing point array. The measured three-dimensional coordinate matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This indicates the measured three-dimensional coordinates of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation.

[0076] In this embodiment, the neural network model is a GA-BP neural network; as Figure 8 As shown, the GA-BP neural network includes an input layer, three hidden layers, and an output layer. The three hidden layers are fully connected, and the distribution of these three hidden layers is designed with 512, 1024, and 512 neurons respectively, all using the ReLU activation function. The number of neurons in the input layer is consistent with the number of sensing points, and the number of neurons in the output layer is three times the number of sensing points, corresponding to the X, Y, and Z coordinate values ​​of each sensing point, and using a linear activation function.

[0077] like Figure 4 As shown, in step 4, the steps for training the selected neural network model using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data are as follows: Step 41: Divide the measured wavelength drift data or measured strain distribution data into training dataset, verification dataset and test dataset according to the corresponding combined working conditions. Each combined working condition data includes all measured wavelength drift data or measured strain distribution data collected under the same combined working condition and its corresponding measured three-dimensional coordinate data. The same combined working condition data is only assigned to one of the training dataset, verification dataset and test dataset.

[0078] In step 41, there are 10 possible combinations of operating conditions. The training data and label data collected under each of the 10 combinations are grouped and divided. Specifically, the data from combinations of operating conditions 1 to 8 are divided into the training dataset, the data from combination of operating condition 9 are divided into the validation dataset, and the data from combination of operating conditions 10 are divided into the test dataset. This ensures that the data used for training, validation, and testing each come from a single combination of operating conditions, thereby avoiding the simultaneous appearance of data from the same combination of operating conditions in the training dataset, validation dataset, and test dataset, and improving the generalization ability of the GA-BP neural network for combinations of operating conditions that were not involved in the training.

[0079] Step 42: Using the training dataset, iteratively optimize the GA-BP neural network based on the genetic algorithm to obtain the optimized initial parameters of the GA-BP neural network, and set the network weights and thresholds of the GA-BP neural network based on the optimized initial parameters.

[0080] In step 42, the genetic algorithm uses only the training dataset to perform a global search on the network weights and thresholds of the GA-BP neural network, avoiding the problem of traditional gradient descent methods easily getting trapped in local optima based on the population evolution mechanism. The genetic algorithm employs an error evaluation criterion mathematically consistent with the loss function of the subsequent backpropagation algorithm. Specifically, it aims to minimize the mean squared error between the measured 3D coordinates represented by the labeled data in the training dataset and the predicted 3D coordinates output by the GA-BP neural network. This mean squared error, or its monotonic transformation, is used as a fitness evaluation index to assess the quality of each individual in the population. The genetic algorithm does not perform gradient backpropagation based on this mean squared error; instead, it iteratively optimizes network weights and thresholds through selection, crossover, and mutation operations based on the fitness evaluation index. In the genetic algorithm settings, the population size is set to 100, the crossover probability to 0.8, and the mutation probability to 0.05. After multiple generations of evolution, optimized initial parameters are obtained and set as the initial state of the GA-BP neural network. The validation and test datasets do not participate in the population evolution optimization process in step S7. The validation dataset is used for hyperparameter optimization and fitting effect judgment during subsequent backpropagation training, while the test dataset is used for actual performance and generalization ability testing after training.

[0081] Step 43: Using the training dataset, update the network weights and thresholds of the GA-BP neural network layer by layer based on the backpropagation algorithm. During the training process, use the validation dataset to optimize the hyperparameters and judge the fitting effect of the GA-BP neural network. Finally, use the test dataset to test the actual performance and generalization ability of the trained GA-BP neural network to complete the training of the GA-BP neural network.

[0082] In step S8, the GA-BP neural network is optimized using the Adam optimizer, with a learning rate set to 0.001 and a batch size of 64 training data used for each backpropagation training.

[0083] Preferably, to prevent overfitting, a Dropout random deactivation mechanism and L2 regularization constraint can be introduced during the backpropagation training of the GA-BP neural network. At the same time, an Early Stopping strategy is used to monitor the loss changes of the validation dataset. When the performance of the neural network no longer improves, the training is terminated early. Then, by comprehensively analyzing the loss curves of the training dataset and the validation dataset, when the mean squared error tends to be stable and there is no obvious oscillation, the neural network is considered to have reached the convergence state.

[0084] The loss function used by the GA-BP neural network during backpropagation training is as follows: in, These are the actual calculated and measured three-dimensional coordinate values. The output of the neural network represents the predicted 3D coordinates, and N is the batch size of the training data used in each backpropagation training.

[0085] The GA-BP neural network does not independently solve for the corresponding predicted 3D coordinates point-by-point based on the wavelength drift or strain of individual sensing points. Instead, it uses the wavelength drift matrix or strain distribution matrix of all sensing points with a fixed spatial topology as model input, and achieves integrated reconstruction of the surface morphology based on the overall distribution characteristics of the sensing point array. Each element in the wavelength drift matrix or strain distribution matrix is ​​mapped one-to-one with the sensing points fixedly arranged in rows and columns on the flexible substrate. This row-column correspondence remains constant during the model training and actual inference phases.

[0086] Even if individual sensing points in the sensing point array exhibit the same wavelength drift or strain, the GA-BP neural network can still distinguish the spatial location of each sensing point and output differentiated three-dimensional coordinate values ​​because each sensing point has a different reference position in the sensing point array, different deformation distributions in the surrounding neighborhood, and independent output channels in the corresponding GA-BP neural network. This overcomes the coordinate mapping confusion caused by overlapping single-point sensing values.

[0087] As a preferred embodiment, the initial three-dimensional coordinate values ​​of each sensing point when the flexible substrate is in a planar state can also be added as auxiliary inputs of the GA-BP neural network; or the GA-BP neural network can be made to output the three-dimensional displacement of each sensing point, and then the three-dimensional displacement matrix can be summed with the initial three-dimensional coordinate values ​​of the corresponding sensing point to finally obtain the predicted three-dimensional coordinate values ​​of each sensing point, thereby further eliminating the technical drawback that a single deformation parameter cannot uniquely match the spatial point position and improving the accuracy of three-dimensional shape reconstruction.

[0088] Step 5: When the flexible substrate is attached to the target element under test, the current wavelength data of the distributed optical fiber sensor is acquired by the signal demodulation system, and the current wavelength drift data or current strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data.

[0089] In step 5, the current wavelength drift data includes the current wavelength drift of each sensing point, and the current strain distribution data includes the current strain of each sensing point; wherein, the current strain of each sensing point is calculated based on the current wavelength drift of the sensing point itself, combined with the relationship function between the wavelength drift and the strain.

[0090] If the measured wavelength drift data is used to train the neural network model in step 4 above, then the current wavelength drift data is used for inference in the subsequent steps, and it is not necessary to convert the current wavelength drift data into the current strain distribution data using the aforementioned relational function in step 5. If the measured strain distribution data is used to train the neural network model in step 4 above, then the current strain distribution data is used for inference in the subsequent steps, and it is necessary to convert the current wavelength drift data into the current strain distribution data using the aforementioned relational function in step 5.

[0091] Step 6: Input the current wavelength drift data or current strain distribution data into the trained neural network model for inference, and receive the predicted three-dimensional coordinate data output by the neural network model.

[0092] In step 6, the current wavelength drift data includes the current wavelength drift matrix of the distributed optical fiber sensor corresponding to the target element under test. The current wavelength drift matrix is ​​composed of the current wavelength drift of each sensing point on the target element under test according to the arrangement of the sensing point array, as shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the current wavelength drift of the sensing point in the m-th row and n-th column.

[0093] Similarly, the current strain distribution data includes the current strain distribution matrix of the distributed optical fiber sensor corresponding to the target element under test. The current strain distribution matrix is ​​composed of the current strain of each sensing point on the target element under test according to the arrangement of the sensing point array, as shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the current strain of the sensor point in row m and column n.

[0094] The predicted three-dimensional coordinate data includes the predicted three-dimensional coordinate matrix of the distributed optical fiber sensor corresponding to the target element under test. The predicted three-dimensional coordinate matrix is ​​composed of the predicted three-dimensional coordinate values ​​of each sensing point output by the neural network according to the arrangement of the sensing point array, as shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the predicted three-dimensional coordinates of the sensor point in the m-th row and n-th column.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and not to limit them. Although the embodiments of the present invention have been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the embodiments of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reconstructing the shape of a flexible curved surface based on a neural network, characterized in that, Includes the following steps: Step 1: Encapsulate the distributed fiber optic sensor in an orthogonal grid pattern within a flexible substrate; Step 2: When the flexible substrate is in a planar state, the initial wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system; Step 3: When the flexible substrate is attached to the calibration surface provided by the calibration element, the measured wavelength data of the distributed optical fiber sensor is acquired by the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. At the same time, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated according to the geometric parameters of the calibration surface. Step 4: Using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data, train the selected neural network model to obtain a trained neural network model. Step 5: When the flexible substrate is attached to the target element under test, the current wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system, and the current wavelength drift data or current strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. Step 6: Input the current wavelength drift data or current strain distribution data into the trained neural network model for inference, and receive the predicted three-dimensional coordinate data output by the neural network model.

2. The flexible curved surface shape reconstruction method according to claim 1, characterized in that, The distributed optical fiber sensor includes a first optical fiber and a second optical fiber. The first optical fiber is bent to form multiple first sensing segments and multiple first connecting segments. Each first sensing segment is parallel to the length direction and arranged sequentially along the width direction. Each first connecting segment connects two adjacent first sensing segments. The second optical fiber is bent to form multiple second sensing segments and multiple second connecting segments. Each second sensing segment is parallel to the width direction and arranged sequentially along the length direction. Each second connecting segment connects two adjacent second sensing segments. The first sensing segments and the second sensing segments are stacked along the thickness direction to form an orthogonal grid structure.

3. The flexible curved surface shape reconstruction method according to claim 2, characterized in that, In step 1, the process of encapsulating the distributed fiber optic sensor within the flexible substrate in an orthogonal grid configuration is as follows: Step 11: Cast and cure a flexible substrate in a flat mold to form a flexible underlayer; Step 12: Lay the first optical fiber flat on the surface of the flexible substrate, and bend the first optical fiber to form multiple first sensing segments and first connecting segments; Step 13: The flexible substrate is cast and cured in the flat mold, on the flexible bottom layer and the first optical fiber to form a flexible intermediate layer; Step 14: Lay the second optical fiber flat on the surface of the flexible intermediate layer, and bend the second optical fiber to form multiple second sensing segments and second connecting segments; Step 15: The flexible substrate is cast and cured in the flat mold, onto the flexible intermediate layer and the second optical fiber, to form a flexible top layer; Step 16: Demold the flexible bottom layer, flexible middle layer and flexible top layer to obtain a flexible substrate encapsulating the distributed optical fiber sensor.

4. The flexible curved surface shape reconstruction method according to claim 1, characterized in that, In step 3, the measured wavelength data of the distributed optical fiber sensor is acquired through the signal demodulation system, and the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor is calculated by combining the initial wavelength data. Simultaneously, the measured three-dimensional coordinate data of the distributed optical fiber sensor is calculated based on the geometric parameters of the calibration surface, as follows: Step 31: Attach the flexible substrate to the calibration surface and adjust the relative position between the flexible substrate and the calibration surface so that the calibration surface is in its initial orientation; Step 32: The distributed optical fiber sensor acquires the measured wavelength data of the calibration surface when it is in the initial orientation through the signal demodulation system, and calculates the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface in combination with the initial wavelength data. At the same time, the three-dimensional coordinate data of the distributed optical fiber sensor when it is in the initial orientation of the calibration surface is calculated according to the geometric parameters of the calibration surface. Step 33: Rotate the calibration surface around its own central normal to other positions according to the preset step rotation angle, so that the flexible substrate deforms as the calibration surface rotates; Step 34: The distributed optical fiber sensor acquires measured wavelength data when the calibration surface is in other orientations using the signal demodulation system, and calculates measured wavelength drift data or measured strain distribution data when the distributed optical fiber sensor is in other orientations using the initial wavelength data. At the same time, the measured three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in other orientations is calculated based on the rotation matrix. Step 35: Repeat steps 33-34 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration surface is in different orientations, as well as the measured three-dimensional coordinate data, are collected. Step 36: Repeat steps 31 and 35 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration elements are in different orientations, as well as the measured three-dimensional coordinate data, are obtained.

5. The flexible curved surface shape reconstruction method according to claim 4, characterized in that, The calibration surface is a standard cylindrical surface. When the calibration surface is in the initial orientation, the center of the calibration surface is aligned with the center of the flexible substrate. The cylindrical arc length direction of the calibration surface is parallel to the length direction of the flexible substrate, and the cylindrical central axis direction of the calibration surface is parallel to the width direction of the flexible substrate. In step 33, when calculating the three-dimensional coordinate data of the distributed optical fiber sensor when the calibration surface is in the initial orientation, the length direction, width direction, and thickness direction of the flexible substrate when it is in a planar state are used as the X-axis direction, Y-axis direction, and Z-axis direction, respectively, to establish a three-dimensional spatial coordinate system. Based on the cylindrical surface parameter equation of the calibration surface, the measured three-dimensional coordinate values ​​of each sensing point in the three-dimensional coordinate system are calculated.

6. The flexible curved surface shape reconstruction method according to claim 5, characterized in that, The geometric parameters of the calibration surface include the cylinder radius. The cylinder diameter, central axis, and central normal of the calibration surface in the initial orientation are respectively used as the X-axis, Y-axis, and Z-axis of the three-dimensional spatial coordinate system. Based on the cylindrical surface parameter equation of the calibration surface, the measured three-dimensional coordinate values ​​of the i-th sensing point when the calibration surface is in the initial orientation are as follows: in, Let the radius of the cylinder be the calibration surface. Let be the central angle parameter of the i-th sensing point in the parametric equation of the cylindrical surface. Let be the axis parameter of the i-th sensing point in the parametric equation of the cylindrical surface.

7. The flexible curved surface shape reconstruction method according to claim 6, characterized in that, The rotation matrix of the calibration surface when rotated to the j-th orientation is shown below: in, The step rotation angle is... Let be the rotation angle between the j-th orientation and the initial orientation; The measured three-dimensional coordinates of the i-th sensing point when the calibration surface is rotated to the j-th orientation are shown below: in, The measured three-dimensional coordinates of the i-th sensing point when it is in the initial orientation on the calibration surface.

8. The flexible curved surface shape reconstruction method according to claim 4, characterized in that, There are multiple calibration elements, and the calibration surfaces of different calibration elements have different geometric parameters; after step 35, the following steps are also included: Step 36: Repeat steps 31 and 35 until the measured wavelength drift data or measured strain distribution data of the distributed optical fiber sensor when the calibration elements are in different orientations, as well as the measured three-dimensional coordinate data, are obtained.

9. The flexible curved surface shape reconstruction method according to claim 1, characterized in that, Each sensing point forms an array of m rows and n columns, where m and n ≥ 2. The measured wavelength drift data includes multiple measured wavelength drift matrices of the distributed optical fiber sensor. Each measured wavelength drift matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured wavelength drift of each sensing point under this combination of conditions according to the arrangement of the sensing point array. The measured wavelength drift matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the measured wavelength shift of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation. Similarly, the measured stress distribution data includes multiple measured stress distribution matrices of the distributed fiber optic sensor. Each measured stress distribution matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured strain of each sensing point under this combination of conditions arranged according to the sensor point array. The measured stress distribution matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This represents the measured strain at the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation. The measured three-dimensional coordinate data includes multiple measured three-dimensional coordinate matrices of the distributed optical fiber sensor. Each measured three-dimensional coordinate matrix corresponds to a combination of conditions between the calibration surface and the orientation, and is composed of the measured three-dimensional coordinate values ​​of each sensing point under this combination of conditions, arranged according to the sensing point array. The measured three-dimensional coordinate matrix corresponding to the k-th calibration surface being in the j-th orientation is shown below: Where m and n are the number of rows and columns of each sensing point, respectively. This indicates the measured three-dimensional coordinates of the sensing point in the m-th row and n-th column when the k-th calibration surface is in the j-th orientation.

10. The flexible curved surface shape reconstruction method according to claim 1, characterized in that, The neural network model is a GA-BP neural network; in step 4, the steps for training the selected neural network model using the measured wavelength drift data or measured strain distribution data as training data and the measured three-dimensional coordinate data as label data are as follows: Step 41: Divide the measured wavelength drift data or measured strain distribution data into training dataset, verification dataset and test dataset according to the corresponding combined working conditions. Each combined working condition data includes all measured wavelength drift data or measured strain distribution data collected under the same combined working condition and its corresponding measured three-dimensional coordinate data. The same combined working condition data is only divided into one of the training dataset, verification dataset and test dataset. Step 42: Using the training dataset, iteratively optimize the GA-BP neural network based on the genetic algorithm to obtain the optimized initial parameters of the GA-BP neural network, and set the network weights and thresholds of the GA-BP neural network based on the optimized initial parameters; Step 43: Using the training dataset, update the network weights and thresholds of the GA-BP neural network layer by layer based on the backpropagation algorithm. During the training process, use the validation dataset to optimize the hyperparameters and judge the fitting effect of the GA-BP neural network. Finally, use the test dataset to test the actual performance and generalization ability of the trained GA-BP neural network to complete the training of the GA-BP neural network.

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