Method for shape sensing of flexible three-dimensional elongated structures based on fiber optic strain sensing

Abstract

The application discloses a flexible three-dimensional slender structure shape sensing method based on an optical fiber strain sensor, and comprises the following steps: arranging a distributed optical fiber sensor on a to-be-measured slender structure; dividing the to-be-measured slender structure into a plurality of units, and each unit is provided with a plurality of sub-regions; introducing an absolute node coordinate method, and obtaining a total strain conversion matrix of each sub-region according to the coordinates of the position of the distributed optical fiber sensor; acquiring linear strain along the arrangement direction at the arrangement position of the distributed optical fiber sensor by using the distributed optical fiber sensor; constructing a correlation algorithm by using the total strain conversion matrix and the measured strain value, so that the coordinates and directions of each node between units can be obtained; and substituting the coordinates of each node into a finite element shape function to obtain the shape of the deformed slender structure. Compared with other existing shape sensing algorithms, the application can realize shape sensing of three-dimensional slender structures with different cross-sectional shapes on the basis of relatively freely designing the optical fiber arrangement scheme.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of distributed optical fiber shape sensing technology, in particular to a flexible three-dimensional slender structure shape sensing method based on optical fiber strain sensing. BACKGROUND

[0002] With the development of smart materials and sensor technology, flexible structure shape sensing and health monitoring based on strain measurement have received extensive attention. In aerospace, the monitoring accuracy of structure deformation is directly related to the performance of space structures, especially for large space antennas; in robotics, efficient shape sensing technology is essential for continuum robots; in the field of medical devices, steering flexible needles and other minimally invasive surgical instruments need to accurately perceive their load and deformation in the human body. For the above application scenarios, distributed fiber sensor network is an effective solution. How to use the measured strain information to reconstruct the deformation of the flexible structure is the core problem of the application of distributed fiber sensor network in flexible structure shape sensing.

[0003] Distributed fiber sensing technology can densely measure the strain of each point on a single mode optical fiber attached to the surface of the structure or embedded in the structure. By using the strain data obtained by the distributed fiber sensor, the real-time deformation state of the structure can be reconstructed through a certain method, which is called shape sensing. The existing shape sensing methods have three problems: (1) the object of shape sensing is usually a slender standard base with a circular cross section, which means that such methods cannot be directly used for actual structures; (2) multiple optical fibers (usually up to 7) are needed to obtain the deformation of the structure, which has certain difficulties in process and cost; (3) it cannot accurately reconstruct the torsion, which only regards the structure torsion as a part that is removed by compensation when reconstructing the bending deformation of the structure. SUMMARY

[0004] The purpose of the present application is to provide a shape sensing method that is aimed at actual structures, has high precision and is relatively low in cost.

[0005] To achieve the above purpose, a flexible three-dimensional slender structure shape sensing method based on optical fiber strain sensing according to the present application comprises:

[0006] Distributed fiber sensor is laid on the slender structure to be measured;

[0007] The slender structure to be measured is divided into a plurality of units, each unit is provided with a plurality of sub-regions; according to the coordinates of the positions of the distributed fiber sensors, the overall strain transformation matrix of each sub-region is obtained;

[0008] The linear strain along the layout direction at the layout position of the distributed fiber sensor is obtained by using the distributed fiber sensor;

[0009] Through the total strain conversion matrix and the measured linear strain value, the coordinates and directions of each node between units are obtained cell by cell;

[0010] The coordinates of each node are substituted into the finite element shape function to obtain the shape of the deformed slender structure.

[0011] Further, the distributed optical fiber sensor layout is determined by the actual structure to be measured, and is fixed in the slender structure to be measured in a certain form such as pasting or embedding.

[0012] Further, the total strain conversion matrix of each sub-region, i.e. the conversion matrix from the unit node coordinates to the strain, is:

[0013]

[0014] Where i is the number of the sub-region within the unit; L i represents the sub-region, i.e. the pasting position of a section of optical fiber within the unit; l is the position of the measuring point in the optical fiber measuring domain; the sub-region is divided in order to relax the point-by-point matching constraint of the measured strain and the theoretical strain to the matching constraint of the strain in the integral sense within the sub-region, and to minimize the calculation difficulty caused by the influence of unmodeled factors on the local strain distribution; is the strain conversion matrix of each point.

[0015] Further, the strain conversion matrix of each point is the linear strain conversion matrix from the unit node coordinates to the direction of the optical fiber arrangement at this point, and the linear strain of any point in a certain direction is written as:

[0016]

[0017] Where v is the Poisson's ratio of the slender structure to be measured, Δl0=[Δl 0x Δl 0y Δl 0z is a unit vector indicating a direction, representing the measurement direction of the optical fiber at this point (i.e. the layout direction of the optical fiber).

[0018] Further, is obtained by introducing an absolute node coordinate space beam element while ignoring the cross-section deformation. The reason for ignoring the cross-section deformation is that this processing can reduce the computational complexity of subsequent solving, and in fact, the contribution of not ignoring the cross-section deformation to the result accuracy is extremely limited, and even leads to computational divergence. Specifically, is written as:

[0019]

[0020] Where, is the strain transformation matrix in a particular direction, x is the axial direction of the structure, y and z are two directions parallel to the cross section of the structure, xx represents the linear strain in the axial direction, xy represents the shear strain in this direction, which are expressed by the following formula:

[0021]

[0022] Where S is the shape function of the element, that is, the interpolation function of the position of each point in the element according to the node coordinates:

[0023] S = [S1I3 S2I3 S3I3 S4I3 S5I3 S6I3 S7I3 S8I3]

[0024] S1 = 1 - 3ξ 2 + 2ξ 3 , S2 = 1(ξ - 2ξ 2 + ξ 3 ), S3 = 1(η - ξη), S4 = 1(ζ - ξζ),

[0025] S5 = 3ξ 2 - 2ξ 3 , S6 = 1(-ξ 2 + ξ 3 ), S7 = 1ξη, S8 = 1ξζ

[0026] ξ = x / l, η = y / l, ζ = z / l

[0027] Where I3 represents the third-order unit matrix, ξ, η, ζ are dimensionless coordinates.

[0028] Further, since the element-by-element solution method is adopted, it means that the coordinates of one end of each element whose node coordinates are required to be solved are known. For each element, the shape sensing problem is described as a nonlinear optimization problem:

[0029]

[0030] This formula is to obtain the best node coordinates that match the theoretical strain (derived from the node coordinates) with the measured strain is the overall strain transformation matrix of each sub-region; ε m (l) is the measured strain value, e is the element node coordinate vector before reduction:

[0031]

[0032] Where r A = [r AX r AY r AZ ], r B = [rBX r BY r BZ [] represents the coordinates of the two endpoints of the element in the global coordinate system; This is the reduced element node coordinate vector for easier solution:

[0033]

[0034] θ A =[θ AX θ AY θ AZ ]、θ B =[θ BX θ BY θ BZ All are Euler angles derived from directional gradients, λ A , λ B These are the elongation rates of the two endpoints, respectively; e and e have a one-to-one correspondence, which is obtained through the formula for converting gradient vectors to Euler angles.

[0035] Furthermore, the coordinates of the other end of each element for which the node coordinates are to be solved are obtained through an iterative Newton-Raphson method:

[0036]

[0037] Where k represents the number of iterations; Given the coordinates of a node at one end of an element, Let these be the coordinates of the other node to be solved; for Currently relative to gradient vector, for Currently relative to The second derivative matrix is ​​obtained; using the above formula, after a finite number of iterations, the node coordinates at the other end of a single unit are obtained. After performing this operation unit by unit, the node coordinates of the entire slender structure to be tested can be obtained.

[0038] Furthermore, the coordinates of a point on the slender structure to be tested are obtained by the following formula:

[0039] r(x0,y0,z0)=S(x0,y0,z0)e

[0040] Where S(x0,y0,z0) is the element shape function, and (x0,y0,z0) represents the position of a point in the structure; from the above formula, the overall shape of the structure is obtained through the overall node coordinates.

[0041] Compared with the prior art, the above technical scheme has the advantages that: 1. The absolute node coordinate unit is introduced into the shape sensing method, the strain of a point on the measured structure in any direction after loading can be relatively accurately described, and the shape sensing problem is constructed into the form of a nonlinear optimization problem. Therefore, the method can be directly compatible with different optical fiber layout configurations and different measured structure section shapes, and can also design an optical fiber layout configuration that is compatible with the actual measurement conditions, has reliability and economy, and is suitable for various engineering conditions. This is more practical and economical than the existing shape sensing method that ensures measurement stability by using a large number of optical fibers.

[0042] 2. The application overcomes the influence of unmodeled factors (such as section warping) on the local strain of the measured structure (this influence reduces the accuracy of shape sensing and even leads to calculation divergence), that is, the measuring points in the unit are divided into multiple sub-regions, and the relationship between the theoretical strain distribution and the actual measurement value is relaxed from point-by-point matching to matching in the integral sense within the sub-regions, which can effectively improve the accuracy of the shape sensing technology. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a flowchart of the method of the application;

[0044] Figure 2 is a schematic diagram of the measured structure and optical fiber layout;

[0045] Figure 3 is a schematic diagram of the division of the measured structure unit;

[0046] Figure 4 is a schematic diagram of the division of the sub-regions;

[0047] Figure 5 is a schematic diagram of the deformed measured structure;

[0048] Figure 6 is a comparison diagram of the actual shape of the measured structure and the shape reconstructed by the method of the application.

[0049] In the figure, 1 is a distributed optical fiber sensor a; 2 is a distributed optical fiber sensor b. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application, that is, the described examples are only a part of the examples of the present application, but not all the examples.

[0051] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0052] Example 1

[0053] like Figure 1 As shown, this application provides a method for shape sensing of flexible three-dimensional slender structures based on fiber optic strain sensing. This method is designed for scenarios requiring the sensing of the deformation state of slender structures undergoing large deformations, and specifically includes:

[0054] S1: Distributed fiber optic sensors are deployed on the slender structure to be tested;

[0055] Specifically, prepare one distributed fiber optic sensor a and one distributed fiber optic sensor b. In this example, considering the characteristics of the object under test (a beam with a variable rhomboid cross-section), as well as economy, accuracy, and reliability of the results, the two distributed fiber optic sensors are attached to the slender structure under test in a double-helix configuration, such as... Figure 2 As shown, the measurement area of ​​the distributed optical fiber sensor is the attached linear area, and it measures the linear strain at each point along the fiber optic cable's direction.

[0056] S2: Divide the slender structure to be tested into multiple units, each unit having several sub-regions; obtain the overall strain transformation matrix of each sub-region based on the coordinates of the distributed fiber optic sensor positions;

[0057] Specifically, considering the actual situation, the slender structure to be tested is divided into 8 units. Each unit is then composed of two distributed optical fiber sensors wound around it twice. Figure 3 As shown; and each 1 / 4 circle is considered a sub-region. Figure 4 The image shows two sub-regions, L1 and L2, divided using this method. Each unit has 16 sub-regions.

[0058] The overall strain transformation matrix for each sub-region is obtained as follows: First, the strain transformation matrix of each point within the measurement range of the distributed fiber optic sensor is calibrated. The position of a point is denoted as P(l0, Δl0), where l0 is the coordinate within the linear region of the fiber optic measurement range, and Δl0 = (Δl0, ... 0x ,Δl 0y ,Δl 0z If the direction of the fiber optic cable at this point is given, then the linear strain ε along the fiber optic cable measurement direction at this point is... t It can be written as:

[0059]

[0060] in

[0061]

[0062]

[0063] Then the overall strain transformation matrix for each sub-region is obtained:

[0064]

[0065] Where L i The sub-regions are defined.

[0066] S3: Using distributed optical fiber sensors, obtain the linear strain along the deployment direction at their deployment location;

[0067] Specifically, for the structure under test that has been subjected to load and has deformed ( Figure 5 The linear strain ε within the linear region where the optical fiber is deployed is obtained through distributed optical fiber sensors. m .

[0068] S4: Using the overall strain transformation matrix and the measured linear strain values, obtain the coordinates and directions of each node between elements on an element-by-element basis;

[0069] Specifically, for each element, the problem of determining its node coordinates can be described by the following formula:

[0070]

[0071] In practice, when solving for each element, the coordinates of one of its nodes are known. Starting from the root element, the coordinates of the nodes at the root end of this element can be written as: The coordinates of the nodes at the other end of this element are obtained through an iterative method using the Newton-Raphson method. The iterative formula is as follows:

[0072]

[0073] in They are respectively Currently relative to The gradient vector and second derivative matrix. In this embodiment, the solution process for all elements is performed in 4 iterations; the gradient vector and second derivative matrix are obtained from the above equation. Then, the iterative formula for the second unit is as follows:

[0074]

[0075] get Then, the solution is applied to the third element. This process is repeated for all elements to obtain the desired result. That is, the node coordinates of the entire structure.

[0076] S5: Substituting the coordinates of each node into the finite element shape function, the shape of the deformed slender structure is obtained:

[0077] Specifically, the reduced node coordinates e are converted into the node coordinates before reduction by the following formula: Ni :

[0078]

[0079] Wherein

[0080]

[0081] After obtaining e Ni , the coordinates of a point P(x0, y0, z0) in the structure can be obtained by the following formula:

[0082] r(x0, y0, z0) = S(x0, y0, z0)e

[0083] S(x0, y0, z0) is the shape function corresponding to this point, which is obtained by the following formula:

[0084] S = [S1I S2I S3I S4I S5I S6I S7I S8I]

[0085] S1 = 1 - 3ξ 2 + 2ξ 3 , S2 = l(ξ - 2ξ 2 + ξ 3 ), S3 = l(η - ξη), S4 = l(ζ - ξζ),

[0086] S5 = 3ξ 2 - 2ξ 3 , S6 = l(-ξ 2 + ξ 3 ), S7 = lξη, S8 = lξζ

[0087] ξ = x0 / l, η = y0 / l, ζ = z0 / l

[0088] At this time, the shape perception of the whole structure to be measured can be completed. The specific effect is as follows: Figure 6 ​It can be seen that the reconstructed deformed shape has no obvious error with the actual deformed shape, so the method can accurately obtain the deformed shape of the structure to be measured. Compared with the traditional shape sensing, the method is more free in the structure section and the fiber arrangement, can be used for non-circular cross-section such as rhombus, and is more economical. By dividing the measuring points in the unit into multiple sub-zones and rewriting the nonlinear optimization problem into a weak form, the relationship between the theoretical strain distribution and the actual measured value is relaxed from point-by-point matching to integral sense matching, and then the influence of unmodeled factors on local strain is eliminated.

[0089] The foregoing description of specific exemplary embodiments of the application has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the application to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain the principles of the application and its practical application and to thereby enable others skilled in the art to best utilize the application and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the application be defined by the claims and their equivalents.

Claims

1. A method for shape sensing of flexible three-dimensional slender structures based on fiber optic strain sensing, characterized in that, The application relates to a method for shape sensing of an elongated structure. The method comprises the following steps: arranging a distributed optical fiber sensor on the elongated structure to be measured; dividing the elongated structure to be measured into a plurality of units, each unit being provided with a plurality of sub-regions; obtaining a total strain conversion matrix of each sub-region according to the coordinates of the distributed optical fiber sensor; obtaining linear strain along the arrangement direction at the arrangement position of the distributed optical fiber sensor by using the distributed optical fiber sensor; obtaining the coordinates and directions of each node between the units by using the total strain conversion matrix and the measured linear strain value; obtaining the shape of the elongated structure after deformation by substituting the coordinates of each node into a finite element shape function; wherein, is the number of sub-regions within a unit; represents a sub-region, i.e. the sticking position of a section of optical fiber within a unit; is the position of a measurement point within the measurement domain of the optical fiber; is the strain conversion matrix for each point; Strain transformation matrix for each point i.e. the linear strain transformation matrix from the unit node coordinates to the fibre orientation at this point, the linear strain in a certain direction at any point is written as: wherein is the Poisson's ratio of the elongated structure material to be measured, is a unit vector indicating a direction, representing the measurement direction of the optical fiber here. Strain transformation matrix for each point is written as: wherein , , is a strain transformation matrix for a specific direction, is the axial direction of the structure, and are two directions parallel to the cross section of the structure, denotes the linear strain in the axial direction, denotes the shear strain in this direction, which are expressed by the following equations: ， wherein is a shape function, i.e. an interpolation function that interpolates the position of a point within an element from the nodal coordinates: wherein represents a three-order unit matrix, , , are dimensionless coordinates.

2. The method according to claim 1, wherein, the total strain conversion matrix of each sub-region is a conversion matrix from the node coordinates to strain, and is as follows:

3. The method of claim 1, wherein the fiber optic strain sensing based shape sensing of a flexible three-dimensional elongate structure is performed by: the distributed optical fiber sensor is fixed on the elongated structure to be measured in a pasting or embedding mode. ​ wherein is the global strain transformation matrix for each sub-region; is the measured strain value, is the unit node coordinate vector before reduction: wherein , is the coordinate of the node of the element in the global coordinate system; is the coordinate of the node of the element in the global coordinate system; , are Euler angles converted from the directional gradient, , are elongation rates of the two end nodes, respectively; and have a one-to-one correspondence, which is obtained by the conversion formula of the gradient vector to the Euler angle.

4. The method according to claim 3, wherein the fiber optic strain sensing based shape sensing of a flexible three-dimensional elongated structure is characterized by, for each unit, the shape sensing problem is described as a nonlinear optimization problem: wherein represents the number of iterations; is the node coordinate of one end of the element known, is the node coordinate of the other end to be solved; is the current gradient vector with respect to , is the current Hessian matrix with respect to ; the coordinates of the other end of each unit requiring to be solved are obtained by using a Newton-Raphson method in an iterative mode:

5. The method according to claim 4, wherein the fiber optic strain sensing based flexible three-dimensional slender structure shape sensing method is characterized by, by using the above formula, the node coordinates of the other end of a single unit are obtained through a limited number of iterations; after the operation is performed on the units, the node coordinates of the whole elongated structure to be measured are obtained. the coordinates of a point of the elongated structure to be measured are obtained by using the following formula: wherein is a unit form function, represents the position of a point in the structure; from the above equation, the overall shape of the structure is obtained by the overall node coordinates.

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