Segmented curvature integral shape sensing method based on local physical closure constraints

Abstract

The application discloses a segmented curvature integral shape sensing method based on local physical closure constraint, which is suitable for local deformation monitoring of large structures such as railways and bridges. The method obtains a discrete curvature data sequence of a measured object along a line; performs a sliding window average operation on the absolute value of the curvature, determines an adaptive detection threshold based on statistical characteristics, and generates a binary detection mask; multiplies the mask with the curvature data to extract an active region, and obtains a feature active interval set through merging and filtering; for each feature active interval, an optimal curvature offset is independently determined based on the boundary physical known state to perform compensation and correction, so that local physical closure is realized; and based on the corrected curvature data, segmented integration and splicing are performed to obtain a complete shape curve. The application corrects the curvature offset from the source, effectively suppresses the secondary integral drift, and realizes long-distance high-precision shape inversion.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic sensing and shape inversion technology, and specifically relates to a piecewise curvature integral shape sensing method based on local physical closure constraints. Background Technology

[0002] Fiber optic shape sensing technology is a class of techniques that reconstructs the geometry of a measured object by measuring strain or curvature information along the fiber optic cable and using integral operations. The basic principle of this technology is to convert discrete curvature data into continuous shape coordinates through tangential angle integration and coordinate integration, thereby reconstructing a planar curve. Existing technologies include multi-core fiber sensing, fiber Bragg grating (FBG) array sensing, and distributed sensing based on optical frequency domain reflection (OFDR). Application scenarios mainly cover the health monitoring of large structures such as railways and bridges, which are predominantly straight sections with localized deformation characteristics. In structural health monitoring, the geometry of the measured object is a key parameter for assessing structural condition, predicting damage, and implementing preventative maintenance; high-precision shape inversion is of great significance for ensuring structural safety.

[0003] However, shape sensing methods based on curvature integrals face a core challenge—the quadratic integral drift problem. Shape inversion requires quadratic integration of curvature data: the first integration yields the tangential angle, and the second integration yields the coordinate position. When there is a small offset Δκ in the original curvature data, the position error accumulates and amplifies according to the squared distance law after quadratic integration, leading to severe distortion in the inversion results. In local deformation monitoring scenarios, this drift manifests as a typical "W-shaped distortion"—that is, unreasonable bulging occurs on both sides of the feature region, the overall baseline exhibits an upward-opening parabolic trend, and significant deviations exist at the boundaries. As the sensing distance increases, the drift error increases sharply, severely limiting the application of the curvature integral method in long-distance scenarios.

[0004] Existing technologies address the aforementioned drift problem primarily through several approaches, but all have significant limitations: First, traditional post-processing detrending methods forcefully eliminate trends and bring boundary deviations to zero through global polynomial fitting. However, this method is purely mathematical and cannot distinguish between effective physical signals and drift errors, thus disrupting the physical continuity of feature regions and introducing artificial distortion. Second, Kalman filtering-based methods, while achieving high-precision shape inversion, are mainly applicable to small-scale scenarios (tens of centimeters), and their effectiveness in long-distance (tens of meters) monitoring scenarios has not been verified. Third, multi-sensor fusion methods rely on external geometric measurement auxiliary equipment such as inertial measurement units (IMUs) and electromagnetic tracking, significantly increasing system complexity and cost, which is unfavorable for large-scale engineering deployment. Furthermore, at the sensing hardware level, a single FBG sensor cannot distinguish the contributions of strain and temperature to wavelength drift, i.e., the temperature-strain cross-sensitivity problem. Existing solutions, such as the reference grating method, require additional sensors, while the thermocouple compensation method increases system complexity. In summary, existing technologies lack a high-precision shape inversion method that can correct curvature integral drift from the source within a long-distance sensing range without the need for external geometric measurement auxiliary equipment. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a piecewise curvature integral shape sensing method based on local physical closure constraints. This method can effectively suppress shape inversion distortion caused by quadratic integral drift, achieve high-precision shape inversion over long-distance sensing ranges, and maintain the physical fidelity of local deformation features. It also has the advantage of not requiring external geometric measurement auxiliary equipment.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A piecewise curvature integral shape sensing method based on local physical closure constraints includes the following steps:

[0008] S1. Obtain the discrete curvature data sequence along the line of the object being measured.

[0009] S2. Perform a sliding window averaging operation on the absolute values ​​of the curvature data sequence to obtain a sliding window absolute mean sequence. Determine an adaptive detection threshold based on the statistical characteristics of the sliding window absolute mean sequence. Compare the sliding window absolute mean sequence with the adaptive detection threshold to generate a binary detection mask. The adaptive detection threshold is determined by calculating the median and standard deviation of the sliding window absolute mean sequence, using the median and α times the standard deviation as the sum, where α is a preset positive constant.

[0010] The beneficial effect of the sliding window absolute mean detection is that when the curvature data crosses the zero point (i.e., the inflection point position), since the sliding window performs an average operation on the absolute value, the absolute mean sequence of the sliding window remains positive at that position, thereby avoiding the inflection point position being misjudged as the interval boundary and ensuring the integrity of the feature region.

[0011] S3. Multiply the binary detection mask with the curvature data sequence to extract active regions, merge adjacent active regions, and filter active regions whose length is less than a preset filtering threshold to obtain a set of feature active regions.

[0012] S4. For each active feature interval in the set of active feature intervals, based on the physically known state of the boundary of the active feature interval, independently determine the optimal curvature offset for compensation and correction to achieve local physical closure. The optimal curvature offset has an analytical solution in closed form, requiring no iterative optimization and exhibiting low computational complexity.

[0013] S5. Based on the corrected curvature data, perform a second integral on the active feature region, set the curvature to zero for the inactive region, and stitch together to obtain the complete shape curve of the object under test.

[0014] The beneficial effects of this invention are as follows:

[0015] (1) Fundamentally suppressing quadratic integral drift: Unlike the traditional post-processing detrending method described in the background art, which forcibly eliminates the trend through global polynomial fitting, this invention independently applies local physical closure constraints to each active feature region, corrects the curvature offset from the source, fundamentally eliminates the "W-shaped distortion" caused by quadratic integral drift, and does not destroy the physical continuity of the feature region.

[0016] (2) Maintaining the physical fidelity of local deformation features: This invention achieves natural closure at the boundary of the interval through local closure constraints, unlike the post-processing detrending method which forcibly eliminates the trend through global polynomial fitting, thus avoiding the destruction of the physical continuity of the feature region and effectively maintaining the authenticity of local deformation features.

[0017] (3) Applicable to long-distance sensing: Unlike the Kalman filtering method described in the background technology, which is only applicable to small-scale scenes, the present invention adopts a segmented processing strategy to independently correct each active feature interval, avoiding the cross-interval accumulation of errors in long-distance integration, and achieving high-precision shape inversion within the long-distance sensing range; at the same time, no external geometric measurement auxiliary equipment (such as inertial measurement unit, electromagnetic tracking, etc.) is required, and the system has low cost and is easy to deploy.

[0018] (4) Temperature self-compensation and sensitivity doubling: In view of the problem that a single FBG sensor cannot distinguish between strain and temperature in the background technology, when combined with parallel dual-fiber flat strip optical cable differential sensing hardware, the strain sensitivity is doubled while eliminating the common mode effect of temperature on wavelength drift by performing differential calculation on the wavelength change of two gratings at the same axial position. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the overall process of a piecewise curvature integral shape sensing method based on local physical closure constraints according to the present invention.

[0020] Figure 2 This is a schematic diagram of the feature interval division principle based on sliding window absolute mean detection of the present invention, wherein (a) is the original curvature signal, the sliding window absolute mean curve and the adaptive detection threshold, (b) is the fragment interval obtained by the initial threshold division, and (c) is the final feature region division after interval merging.

[0021] Figure 3 This is a schematic diagram of the local physical closure constraint correction principle of the present invention, where (a) is a comparison before and after curvature domain correction, and (b) is a comparison of shape domain integral closure effect.

[0022] Figure 4 The diagram shows the parallel dual-fiber flat ribbon optical cable structure and differential measurement principle of the present invention, wherein (a) is a schematic diagram of the cross-sectional structure, (b) is a schematic diagram of the differential measurement principle, and (c) is a schematic diagram of the installation. Detailed Implementation

[0023] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Based on the embodiments of the present invention, all equivalent embodiments obtained by those skilled in the art without inventive effort are within the protection scope of the present invention.

[0024] The following is combined Figures 1 to 4 Taking the monitoring of local deformation of railway tracks as an example, the specific implementation of the present invention will be described in detail.

[0025] like Figure 1 As shown, this invention discloses a piecewise curvature integral shape sensing method based on local physical closure constraints. The overall process includes five steps: acquiring discrete curvature data sequences, sliding window absolute mean detection, interval merging and filtering, local physical closure constraint correction, piecewise integration and result concatenation. The implementation details of each step are described in detail below.

[0026] In this embodiment, the sensing system uses a flat strip optical cable 5 to acquire curvature data. For example... Figure 4As shown in (a), the flat ribbon optical cable 5 consists of a protective layer 1, a flexible flat ribbon support material 2, a weak fiber Bragg grating (wFBG) array fiber 3, and a wFBG array fiber 4. The wFBG array fiber 3 and wFBG array fiber 4 are encapsulated parallel and symmetrically on both sides of the flexible flat ribbon support material 2, and the grating positions are strictly one-to-one in the axial direction. The protective layer 1 wraps around the flexible flat ribbon support material 2 and the wFBG array fibers 3 and 4, providing moisture protection, corrosion protection, and mechanical protection.

[0027] In this embodiment, the flat ribbon optical cable 5 has a total sensing length of approximately 22.4m and contains a total of 224 FBG sensors (the wFBG array fiber 3 and wFBG array fiber 4 each contain 112 sensing nodes). The spacing between adjacent FBGs is 200mm, and the spacing between the two fibers is approximately 12mm. The flat ribbon optical cable 5 is as follows... Figure 4 (c) is attached to the surface of the test object 6 as shown, and arranged along the axial direction of the test object 6.

[0028] This invention utilizes a flat-ribbon optical cable 5 for differential measurement to obtain curvature data. When the FBG is subjected to axial strain or temperature changes, its Bragg wavelength drifts, and a single FBG cannot distinguish the contributions of strain and temperature, resulting in a temperature-strain cross-sensitivity problem. Therefore, this invention utilizes symmetrically encapsulated wFBG array fibers 3 and 4 within the flat-ribbon optical cable 5 for differential measurement, with the sensing principle as follows: Figure 4 As shown in (b): When the flat ribbon optical cable 5 is bent, the two optical fibers are subjected to tension and compression respectively, with equal but opposite strain values; since they are made of the same material and are in the same environment, their temperature sensitivity is the same. By subtracting the wavelength changes of two corresponding gratings at the same axial position, the common-mode effect of temperature can be eliminated simultaneously, and the strain sensitivity can be doubled, resulting in a differential wavelength signal. With axial strain Relationship:

[0029] (1)

[0030] In equation (1), This is the strain sensitivity coefficient.

[0031] According to mechanics of materials, when the flat ribbon optical cable 5 bends with the substrate, since the wFBG array fiber 3 and wFBG array fiber 4 are symmetrically distributed on both sides of the neutral axis, their distances from the neutral axis are all... ( The distance between the two optical fibers (i.e., the width of the flat ribbon cable) shows a linear relationship between the axial strain caused by bending and the change in curvature. Substitute into equation (1) and denote the curvature proportionality coefficient. The correspondence between the differential wavelength signal and the curvature can be obtained:

[0032] (2)

[0033] In equation (2), The parameters are uniquely determined by the inherent physical parameters of the sensor and can be determined through a combination of theoretical calculations and experimental calibration.

[0034] In this embodiment, the optimal curvature ratio coefficient is obtained through experimental calibration. m⁻¹ / nm, this calibration value is used for subsequent shape inversion and curvature conversion. Through the above differential measurement and curvature conversion, a discrete curvature data sequence along the measured object is obtained. ,in Step S1 is completed by indexing discrete positions along the fiber axis.

[0035] After obtaining the discrete curvature data sequence, steps S2 to S5 are executed to complete the shape inversion. The core idea of ​​this invention is: in the flat region of the measured object (where the curvature is theoretically zero), the physical prior of "zero curvature" is used to correct the integral drift; for the active feature regions with deformation, the curvature offset is corrected from the source by applying local physical closure constraints, so that the integral results in each interval achieve natural closure.

[0036] Step S2: Sliding window absolute mean detection. For example... Figure 2 As shown in (a), the curvature data sequence The absolute values ​​are averaged using a sliding window to obtain a sequence of absolute mean values ​​for the sliding window. The size of the sliding window... The sensor's spatial resolution and the scale of the feature region are used as the basis for setting the adaptive detection threshold. The threshold is determined based on the statistical properties of the sliding window absolute mean sequence: the median and standard deviation of the sliding window absolute mean sequence are calculated, and the median is used as the threshold value. The sum of multiples of the standard deviations is used as the adaptive detection threshold (in this embodiment, the preset normal coefficients). Preferably, the constant is 0.5. It should be understood that, depending on the signal characteristics under different noise environments, the constant... (This can be flexibly adjusted according to the actual project situation and is not limited to this embodiment). The absolute mean sequence of the sliding window is compared with the adaptive detection threshold. Regions greater than the threshold are marked as 1, and regions less than the threshold are marked as 0, thus generating a binary detection mask.

[0037] The beneficial effect of the sliding window absolute mean detection is that when the curvature data crosses the zero point (i.e., the inflection point) within the feature region, the absolute mean sequence of the sliding window remains positive at that position because the sliding window performs an averaging operation on the absolute value. This avoids the inflection point being misjudged as the interval boundary, ensuring the integrity of the feature region. If the original curvature data is directly thresholded, a "break" will occur at the inflection point, dividing a complete feature region into multiple fragmented intervals, which seriously affects the accuracy of subsequent processing.

[0038] Step S3: Interval merging and filtering. For example... Figure 2 As shown in (b) and (c), the binary detection mask is multiplied by the original curvature data sequence to extract active regions. Since there may be brief zero-value gaps near the inflection point, adjacent active regions are merged (intervals with an interval less than a preset merging threshold are merged), and noise regions with a length less than a preset filtering threshold are filtered to obtain the final set of feature active regions.

[0039] Step S4: Local Physical Closure Constraint Correction. For each active feature region in the set of active feature regions, based on the known physical state of the boundary of the active feature region, the optimal curvature offset is independently determined for compensation correction to achieve local physical closure. In this embodiment, the known physical state is: the two ends of the local deformation region of the measured object (railway) are fixed on a rigid base, and the ordinates of the start and end points of the active feature region are equal after deformation. In the shape inversion based on curvature integral, the formulas for calculating the tangential angle and coordinates are:

[0040] (3)

[0041] (4)

[0042] (5)

[0043] Equation (3) is the integral formula for the tangential angle, where For position Tangential angle at that point This is the initial tangential angle (this value is 0 for a test object that is initially flat). For position The curvature value at the point; Equations (4) and (5) are coordinate integral formulas, and Positions The x and y coordinates of the location, and These are the initial position coordinates.

[0044] like Figure 3 As shown in (a), when there is a small offset in the original curvature data At that time, by applying a constant offset to the original curvature Compensation and correction can eliminate curvature shift at its source. For example... Figure 3 As shown in (b), it can be seen from equation (5) that the vertical coordinate error, after a second integration, accumulates and amplifies according to the law of squared distance: position Error of ordinate at point ,in This is the curvature offset. The integral distance is used. This drift causes "W-shaped distortion" in the inversion results of traditional methods—unreasonable bulging on both sides of the feature region. However, the shape corrected by the method of this invention achieves natural closure, eliminating the W-shaped distortion.

[0045] For the There are three active feature intervals, and a constant curvature offset is applied within each interval. From equations (3) and (5), it can be seen that the change in tangential angle caused by this offset is: This leads to a change in the vertical axis. .

[0046] in, For the first Tangential angle within the active region of each feature For the first The interval length of each active feature interval. Within this interval The average value. Therefore, the corrected endpoint ordinate of this interval is... .

[0047] in, For the first The endpoint ordinate of each active feature interval is obtained by integrating the original curvature data. In a local coordinate system with the origin of this active feature interval, let... That is, after correction, the ordinate of the endpoint equals the ordinate of the starting point (achieving local physical closure), and the analytical solution for the optimal curvature offset can be obtained:

[0048] (6)

[0049] In equation (6), For the first The optimal curvature offset for each active feature region It can be directly calculated from the first integral result of the original curvature data. When the tangential angle within the interval... When smaller, Equation (6) simplifies to This analytical solution requires no iterative optimization, has low computational complexity, and is suitable for real-time or near-real-time monitoring scenarios.

[0050] Step S5: Segmented integration and result stitching. Based on the corrected curvature data, perform a second integration on the active feature regions using the corrected curvature; set the curvature to zero for flat regions (inactive regions); finally, stitch the processing results of each region together to form the complete shape curve of the measured object.

[0051] To verify the effectiveness of the method of this invention, a railway track local deformation simulation experimental platform was constructed. The experimental object was a standard steel square tube, used to simulate the local deformation of the track at the pit location during service. By inserting pads of different thicknesses at different positions at the bottom of the square tube, local lifting of the tube was induced. A total of 10 local deformation conditions with different lifting amounts were set, ranging from 3mm to 46mm. An electric sliding rail laser ranging system was used as the benchmark measurement method for shape inversion.

[0052] Shape inversion was performed using both the traditional quadratic integral method and the piecewise curvature integral method based on local physical closure constraints proposed in this invention. The preprocessed laser scanning data was used as a benchmark for quantitative comparison, and the root mean square error (RMSE) was used to quantify the absolute deviation between the inverted shape and the benchmark shape.

[0053] Experimental results show that the method of this invention reduces the average RMSE of 10 working conditions from 7.98 mm in the traditional quadratic integral method to 0.59 mm, a reduction of approximately 13.5 times. Regarding feature fidelity, the method of this invention achieves an average Pearson correlation coefficient R of 0.9932, and the boundary deviation is reduced from a significant deviation in the traditional method to zero, achieving complete natural closure.

[0054] Regarding measurement repeatability, data were independently collected 10 times each for two operating conditions: a minimum lift of 3 mm and a maximum lift of 46 mm, and the results were compared. The results show that both operating conditions exhibit good consistency in the flat region; in the peak region, repeatability fluctuations are concentrated within a few millimeters. The main source of this repeatability fluctuation is the wavelength accuracy limit of the FBG demodulator, which, after double integration, accumulates to a position uncertainty on the order of several millimeters over long sensing distances.

[0055] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be within the scope of protection of the present invention.

Claims

1. A piecewise curvature integral shape sensing method based on local physical closure constraints, characterized in that, Includes the following steps: The first step is to acquire a discrete curvature data sequence along the line of the object under test. The second step is to perform a sliding window averaging operation on the absolute values ​​of the curvature data sequence to obtain a sliding window absolute mean sequence. Based on the statistical characteristics of the sliding window absolute mean sequence, an adaptive detection threshold is determined. The sliding window absolute mean sequence is compared with the adaptive detection threshold to generate a binary detection mask. The third step is to multiply the binary detection mask with the curvature data sequence to extract active regions. Adjacent active regions are merged, and active regions with a length less than a preset filtering threshold are filtered to obtain a set of feature active regions. The fourth step is to independently determine the optimal curvature offset for each active feature region in the set of active feature regions based on the known physical state of the boundary of the active feature region, and make compensation corrections to achieve local physical closure. The fifth step involves performing a second integral on the active feature regions based on the corrected curvature data, setting the curvature to zero for the inactive regions, and stitching together the complete shape curve of the object under test.

2. The method according to claim 1, characterized in that, The method for determining the adaptive detection threshold in step S2 is as follows: calculate the median and standard deviation of the absolute mean sequence of the sliding window, and use the sum of the median and α times the standard deviation as the adaptive detection threshold, where α is a preset normal number.

3. The method according to claim 1, characterized in that, The known physical state described in step S4 is that, after integrating the corrected curvature data, the ordinates of the start and end points of the active region of this feature are equal.

4. The method according to claim 3, characterized in that, The optimal curvature offset mentioned in step S4 is determined based on the following formula: .in, For the first The optimal curvature offset for each active feature region The index of the active region is used. For the first Tangential angle within the active region of each feature Within this interval The average value, For the first The active feature intervals are based on the endpoint ordinates obtained by integrating the original curvature data. For the first The length of each active feature interval.

5. The method according to claim 3, characterized in that, The step S4 describes independently determining the optimal curvature offset as follows: under the condition that the corrected curvature offset is a constant, the optimal constant offset is calculated to make the corrected endpoint ordinate of the active feature region zero in the local coordinate system with its origin as the origin.

6. The method according to claim 1, characterized in that, The discrete curvature data sequence in step S1 is obtained by arranging a fiber Bragg grating sensor array along the axis of the object being measured, obtaining the wavelength drift of each sensing point, and converting the discrete curvature data sequence through the linear proportional relationship between the wavelength drift and the curvature.

7. A piecewise curvature integral shape sensing system based on local physical closure constraints, characterized in that, include: The curvature acquisition module is used to acquire discrete curvature data sequences along the line of the object being measured; The feature detection module is used to perform a sliding window averaging operation on the absolute values ​​of the curvature data sequence to obtain a sliding window absolute mean sequence, determine an adaptive detection threshold based on the statistical characteristics of the sliding window absolute mean sequence, and compare the sliding window absolute mean sequence with the adaptive detection threshold to generate a binary detection mask. The interval processing module is used to multiply the binary detection mask with the curvature data sequence to extract active regions, merge adjacent active intervals and filter noise intervals to obtain a set of feature active intervals; The local closure correction module is used to independently determine the optimal curvature offset for each active feature region based on the physically known state of the boundary of the active feature region, and to compensate and correct it to achieve local physical closure. The shape stitching module is used to perform a second integral on the active feature regions based on the corrected curvature data, set the curvature to zero for the inactive regions, and stitch together the complete shape curve of the object under test.

8. The system according to claim 7, characterized in that, The curvature acquisition module includes a parallel dual-fiber flat ribbon optical cable sensor, which includes two fiber Bragg grating array fibers. The two fibers are parallel and symmetrically encapsulated on both sides of a flexible flat ribbon support material. The differential wavelength signal is obtained by performing differential calculation on the wavelength change of the two gratings at the same axial position. The discrete curvature data sequence is obtained based on the linear proportional relationship between the differential wavelength signal and the curvature.

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