KR101369869B1 - Localization method of a object using fbg strain sensors - Google Patents

Abstract

Disclosed is a method for estimating the three-dimensional location an object using an FGB strain sensor. According to the present invention, the method for estimating the three-dimensional location an object comprises: a step of installing at least one FGP strain sensor in an object to be wound on the outer surface of the object in a spiral shape; a step of dividing the tensile modulus measured in the FGB strain sensor into the horizontal modulus and the vertical tensile modulus; a step of calculating the strain rate of the object using the horizontal and vertical modulus; and a step of estimating the profile of the object using the strain rate.

Description

3D Position Estimation Method of an Object Using a Pp Strain Sensor

The present invention relates to a method for estimating a three-dimensional position of an object to be detected, such as a cable. A method for estimating dimensional position.

In general, an optical fiber sensor is a sensor for estimating a measurement amount using an intensity of an optical signal (light) passing through an optical fiber, a refractive index and a length of an optical fiber, a mode, and a change in polarization state. According to the effect, it is classified into intensity type, phase type, diffraction grating type, mode modulation type, polarization type, distribution measuring type and the like. Recently, optical fiber sensors have been applied to measurement of various objects such as voltage, current, temperature, pressure, strain, turnover, sound, and gas concentration. In particular, the optical fiber sensor is capable of ultra-precise wideband measurement, is not affected by electromagnetic waves, is easy to measure remotely, does not use electricity in the sensor unit, and has excellent corrosion resistance of silica, so there are few restrictions on the use environment. There is a technical advantage, the field of use is expanding rapidly.

Fiber Bragg Grating (FGB) strain sensor or FBG sensor is a kind of optical fiber sensor as described above, and several optical fiber Bragg gratings are engrave on the optical fiber in a certain way, and then in each grating according to changes in external environmental conditions such as temperature and intensity It is a sensor using the characteristic that the wavelength of reflected light is changed. The FGB strain sensor is mainly applied to the diagnosis of the condition of structures. For example, when manufacturing a bridge, a dam, a building, etc., a FGB strain sensor is installed in concrete, and a structure safety diagnosis method of detecting a tension distribution or bending degree inside a structure through an FGB strain sensor has been known.

Embodiments of the present invention provide a method for estimating a three-dimensional position of an object using an FGB strain sensor that can quickly and accurately estimate a three-dimensional profile of an object such as a cable using an FGB strain sensor.

According to an aspect of the present invention, at least one FGB strain sensor is installed on the object to be detected, wherein the FGB strain sensor is installed to spirally wound on an outer circumferential surface of the object to be detected; Decomposing the tensile rate measured by the FGB strain sensor into a horizontal tensile rate and a vertical tensile rate; Calculating a strain of the object to be detected based on the horizontal tension rate and the vertical tension rate; Estimating the profile of the target object through the strain; may include a three-dimensional position estimation method of the target object using the FGB strain sensor.

In the three-dimensional position estimation method of the detected object using the FGB strain sensor according to the present embodiment, it is possible to accurately and quickly estimate the profile or three-dimensional position of the cable through a plurality of FBG strain sensors spirally wound on the cable. have.

1 is a general flowchart showing a three-dimensional position estimation method of the object to be detected using the FGB strain sensor according to an embodiment of the present invention.
Figure 2 is a schematic diagram showing the installation of the FBG strain sensor on the cable.
3 is a view showing a state in which the outer peripheral surface of the cable wound the FBG strain sensor is developed in a plan view.
4 is a diagram showing the change of each stress triangle when deformation occurs in the cable.
5 is a diagram showing the vertical tension of each FBG strain sensor as a vertical vector with respect to the cross section.
FIG. 6 is a test result of a location estimation method according to an embodiment of the present invention, tested according to the number of sampling nodes (N = 32, 64, 128, 256).

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. It is to be understood, however, that the following examples are provided to facilitate understanding of the present invention, and the scope of the present invention is not limited to the following examples. In addition, the following embodiments are provided to explain the present invention more fully to those skilled in the art and those skilled in the art will appreciate that those skilled in the art, Will be omitted.

1 is a general flowchart showing a three-dimensional position estimation method of the object to be detected using the FGB strain sensor according to an embodiment of the present invention. Referring to FIG. 1, a three-dimensional position estimation method (hereinafter, referred to as a 'position estimation method') of an object using an FGB strain sensor according to the present embodiment includes installing an FGB strain sensor on an object to be detected. (S1), measuring the tensile rate from the installed FGB strain sensor and decomposing it into horizontal and vertical tensile rates (S2 to S4), calculating strains of the cable and centerline (S5 to S6), cable and centerline It can be configured to include the step of calculating the profile of (S7 to S8).

Hereinafter, each step will be described in more detail.

One. On the subject FGB  Steps to Install a Strain Sensor

The position estimation method according to the present embodiment may include installing an FBG strain sensor on the object to be detected.

The detected object may have a form extending in the longitudinal direction. Alternatively, the detected object may have an elongated form. In addition, the detected object may have a circular cross section. For example, the detected object may include a cable. Hereinafter, for convenience of description, the case where the detected object is a cable will be described by way of example. However, the position estimation method according to the present embodiment can be used to estimate the three-dimensional position of not only the cable exemplified above but also various kinds of objects to be treated in the same manner.

FIG. 2 is a schematic view showing a state in which the FBG strain sensor F is installed in the cable P. Referring to FIG. 2, the FBG strain sensor F may be installed on an outer circumferential surface of the cable P. Referring to FIG. In addition, a plurality of FBG strain sensors (F) may be installed in the cable (P). For example, as illustrated in FIG. 2, the FBG strain sensor F may be installed in three cables P. As shown in FIG.

However, the number of FBG strain sensors installed in the cable may be increased or decreased as necessary. For example, if desired, four strands of FBG strain sensor may be installed in the cable, and more FBG strain sensors may be installed in the cable. In this case, the three-dimensional position estimation of the cable through the FBG strain sensor can be performed similarly to the three-strand case described below. Also, if desired, only two strands of FBG strain sensors can be installed in the cable. In such a case, by interpolating the tensile rate of the virtual FBG strain sensor through interpolation or the like, the position of the cable can be estimated similarly to the case of the three strands described below.

Hereinafter, for convenience of description, a case in which three FBG strain sensors F1, F2, and F3 are installed in the cable P will be described as illustrated in FIG. 2. In addition, as shown in FIG. 2, the FBG strain sensor F1 indicated by the red line represents the first FBG strain sensor F1, the FBG strain sensor F2 indicated by the green line represents the second FBG strain sensor F2, The FBG strain sensor F3 indicated by the blue line will be referred to as a third FBG strain sensor F3.

The first to third FBG strain sensors F may be formed of the same optical fiber. In addition, the first to third FBG strain sensors F1, F2, and F3 may be wound in a helical shape on the outer circumferential surface of the cable P, respectively. In this case, the first to third FBG strain sensors F1, F2, and F3 may be wound around the cable P at the same pitch or twisting rate. The twist rate may refer to the degree to which the first to third FBG strain sensors F1, F2, and F3 are twisted per unit length on the outer circumferential surface of the cable P. In the initial installation state, the twist rates of the first to third FBG strain sensors F1, F2, and F3 will be referred to as 'initial twist rate t ₀ '.

On the other hand, the first to third FBG strain sensors (F1, F2, F3) may be wound on the outer circumferential surface of the cable (P) at regular intervals, and may be arranged symmetrically on the cross-section. In other words, in the initial installation state without the deformation of the cable P, the first to third FBG strain sensors F1, F2, F3 have a certain angular interval (i.e., the bone pattern) from the center line C of the cable P as the origin. In the case of an embodiment, it may be arranged at intervals of 120 degrees. In addition, the first to third FBG strain sensors F1, F2, and F3 may be spaced apart from each other by a center radius r _c on the center line C on the cross section.

2. FGB  Of sensor Tensile modulus  Disassembly steps

Figure 3 shows a state in which the outer circumferential surface of the cable wound the FBG strain sensor is deployed in a plan view. Referring to FIG. 3, the first to third FBG strain sensors F1, F2, and F3 may be arranged to form a predetermined slope on an unfolded plane. In this case, 'stress triangles T1, T2, and T3' may be defined at each sampling node s _p . That is, when the focus is on the first FBG strain sensor F1, a virtual triangle T1 may be defined to the right of the sampling node s _p on the first FBG strain sensor F1. The virtual triangle T1 may be formed by using a portion of the first FBG strain sensor F1 as an hypotenuse. For convenience of description, the virtual triangle T1 defined in the first FBG strain sensor F1 will be referred to as a 'first stress triangle T1'. In a similar manner, the second and third FBG strain sensors ( Second and third stress triangles T2 and T3 may also be defined in F2 and F3.

FIG. 4 illustrates the change of the stress triangles T1, T2, and T3 when deformation occurs in the cable P. Referring to FIG. 4, the hypotenuse lengths of the stress triangles T1, T2, and T3 are illustrated in FIG. 4. It can be seen that is changed according to the horizontal or vertical movement of the upper vertex.

If it is assumed that only pure twisting deformation occurs in the cable P, the upper vertices of each of the stress triangles T1, T2, and T3 are moved only in the horizontal direction. In other words, each of the stress triangles T1, T2, and T3 has only the base length changed. In addition, referring to FIG. 3, when only pure twist deformation occurs, each of the stress triangles T1, T2, and T3 is equally deformed in the horizontal direction. Therefore, the twisting deformation of the cable P can be reflected through the horizontal change of each stress triangle T1, T2, T3, which in turn means that the horizontal tensile rate of each FBG strain sensor F1, F2, F3 ( η).

On the other hand, assuming that only pure bending deformation occurs in the cable P, the top vertices of each of the stress triangles T1, T2, and T3 are moved only in the vertical direction. In other words, each of the stress triangles T1, T2, and T3 is changed only in the length of the height. However, unlike the case where only the pure twist deformation is generated, the vertical deformation of the stress triangles T1, T2, and T3 may be different depending on the direction of the bending deformation. As a result, the bending deformation of the cable P can be reflected through the vertical change of each stress triangle T1, T2, and T3, which in turn means that the vertical tensile rate of each FBG strain sensor F1, F2, F3 is is represented by (e _r , e _g , e _b ). However, the vertical tensile modulus (e _r , e _g , e _b ) may be different from each FBG strain sensor F1, F2, F3 depending on the direction of bending deformation. For convenience of description, the vertical tensile modulus e _r , e _g , e _{b of} the first to third FBG strain sensors F1, F2, F3 are respectively set to the first to third vertical tensile modulus e _r , e. _g , e _b ).

The longitudinal tension (ε _r , ε _g , ε _b ) or stress of each FBG strain sensor (F1, F2, F3) is the wavelength spectrum received at each FBG strain sensor (F1, F2, F3). can be obtained through a spectrum. This is well known in the art and will not be described in detail.

By the Pythagorean theorem as shown in FIG. 4, the vertical tensile modulus e _r , e _g , e _{b of} each FBG strain sensor F1, F2, F3 may be expressed as Equation 1 below.

__________(식 1)

__________ (Equation 1)

In Equation 1, ε _r , ε _g , and ε _b represent the longitudinal tensile rates of the first to third FBG strain sensors F1, F2, and F3, respectively. For convenience of explanation, ε _r is referred to as the first longitudinal tensile modulus (ε _r ), ε _g is the second longitudinal tensile modulus (ε _g ), and ε _b is referred to as the third longitudinal tensile modulus (ε _b ). Shall be. The first to third longitudinal tensile rates ε _r , ε _g , ε _b can be given by measured values of the first to third FBG strain sensors F1, F2, F3. In addition, l, d, and h represent the hypotenuse, the base side, and the height length of each stress triangle T1, T2, and T3 in the absence of deformation.

On the other hand, e _r , e _g , e _b represent the vertical tensile ratios of the first to third FBG strain sensors F1, F2, and F3, respectively. That is, e _r represents a first vertical tensile modulus e _r , e _g a second vertical tensile modulus e _g , and e _b a third vertical tensile modulus e _b . In addition, (eta) represents the horizontal tension rate of the 1st-3rd FBG strain sensor F1, F2, F3. As described above, the horizontal tensile modulus η of the first to third FBG strain sensors F1, F2, and F3 may be the same.

FIG. 5 shows the vertical tensile modulus e _r , e _g , e _b of each FBG strain sensor F1, F2, F3 as a vertical vector with respect to the cross section. Referring to FIG. 5, each FBG strain sensor ( The vertical tensile modulus (e _r , e _g , e _b ) of F1, F2, F3) may be represented by R, G, and B position vectors as shown in Equation 2 below.

__________(식 2)

__________ (Equation 2)

In Equation 2, R, G, and B represent position vectors of the first to third vertical tensile moduli (e _r , e _g , e _b ), respectively, and r _c represents each FBG strain wound on the cable P. The center radius of the sensors F1, F2, F3 is shown.

In this case, assuming that the cross section is maintained in any deformation case, the R, G, and B vectors and the center point O exist on one plane, which can be expressed by Equation 3 below.

__________(식 3)

__________ (Equation 3)

In the cross section shown in FIG. 2, when the position of the first FBG strain sensor F1 is set in the x-axis direction, the first to third center angles θ _r , of the first to third FBG strain sensors F1, F2, and F3 are set. Since θ _g andθ _b are 0, 2π / 3, and 4π / 3, respectively, the center angles (θ _r , θ _g , θ _b ) and center point O are substituted into Equation 3 to obtain Equation 4 below. Can be.

__________(식 4)

__________ (Equation 4)

Through Equation 1 and Equation 4 described above, the first to third longitudinal tensile moduli (ε _r , ε _g , ε _b ) are the first to third vertical tensile moduli (e _r , e _g , e _b ). And, in the horizontal tensile modulus (η).

On the other hand, the initial value of the horizontal tensile modulus (η) for Newton-Raphson interaction can be expressed as shown in Equation 5 below.

__________(식 5)

__________ (Equation 5)

In Equation 5, ε _m may be selected as the smallest value among the first to third longitudinal tensile moduli (ε _r , ε _g , ε _b ).

3. Calculate strain of cable and centerline

Assuming that the centerline C of the cable P is not stretched in the longitudinal direction, the strain at each point of the centerline C is the curvature, k, the twisting, t and the bending direction ( φ).

The bending rate κ may mean a tangential rotation rate of the center line C, and the twist rate t may mean a rotation rate about the center line C. FIG. In addition, the bending direction φ may mean an angle of the cross section in which the center line C is bent.

As described above, when the horizontal tensile rate η is calculated, the twist rate t at the sampling node may be derived by Equation 6 below.

__________(식 6)

__________ (Equation 6)

In Equation 6, t ₀ represents the initial twist rates of the first to third FBG strain sensors F1, F2, and F3.

In addition, the bending direction φ of the cable P may be derived through the direction of a normal vector N projected onto the RGB plane on the cross section (see FIG. 5). The direction of the normal vector N in the RGB plane may be given by Equation 7 below.

__________(식 7)

__________ (Equation 7)

In addition, summarizing Equation 7 above may yield Equation 8 below.

__________(식 8)

__________ (Equation 8)

Therefore, the bending direction φ can be expressed as in Equation 9 below.

__________(식 9)

__________ (Equation 9)

Meanwhile, the bending rate κ of the cable P may be derived as shown in Equation 10 by Euler-Bernoulli beam theory.

__________(식 10)

__________ (Equation 10)

In Equation 10, e _i may be selected from any of the first to third vertical tensile modulus (e _r , e _g , e _b ), and θ _i is the first to third center angle (θ _r , θ _g , θ _b ) can be selected.

The bending rate κ of the cable P centerline C is the rotation rate of the tangential vector of the centerline C, which is the same as the bending rate κ of the cable P derived above.

In addition, the torsion rate τ of the center line C of the cable P may be defined by the rotation rate of the binormal vector. That is, as shown in Equation 11 below, it may be estimated through the sum of the rotation rates of the twist rate t and the bending angle φ.

__________(식 11)

__________ (Equation 11)

4. Profile of centerline and cable ( profile ) Step

An initial position and a Frenet-Serret frame of the cable P may be given by Equation 12 below.

__________(식 12)

__________ (Equation 12)

In addition, through the Frene-Serre formula, the unit tangent vector (T), the unit normal vector (N), the unit vertical normal vector (T) can be derived as shown in Equation 13.

__________(식 13)

__________ (Equation 13)

The profile of the centerline C of the cable P can be obtained by integrating the tangent vector T of each point (node) by the length as shown in Equation 14 below.

__________(식 14)

__________ (Equation 14)

In addition, the actual profile of each spirally wound FBG strain sensor (F1, F2, F3) causes the normal vector (N) of the cable (P) centerline (C) to be reversed by the bending direction angle with respect to the tangential vector (T). Can be obtained.

On the other hand, in the above it is assumed that the center line (C) of the cable (P) is not stretched in the longitudinal direction, if necessary, the longitudinal stretch of the center line (C) of the cable (P) can be considered. In this case, a fourth FBG strain sensor (not shown) may be further installed along the center line C of the cable P, and the length of the cable P center line C may be installed through the fourth FBG strain sensor. Direction, the central tensile modulus ε _c is obtained (see FIG. 2).

In this case, the above-described equations 4, 6, 9, and 10 may be modified as in Equation 15 below.

__________(식 15)

__________ (Equation 15)

In Equation 15, ε _c represents the central tensile rate in the longitudinal direction of the cable P center line C obtained through the fourth FBG strain sensor.

As described above, the position estimation method according to the present embodiment can quickly estimate the profile or three-dimensional position of the cable through a plurality of FBG strain sensors wound spirally around the cable. 6 is a test result of a position estimation method according to an embodiment of the present invention according to the number of sampling nodes (N = 32, 64, 128, 256). Referring to FIG. 6, the number of sampling nodes is increased. It can be seen that the profile of the cable is estimated with high accuracy.

In particular, the position estimation method according to the present embodiment has a technical advantage in that the profile or three-dimensional position of the cable can be estimated in real time through the tensile rate (or stress) measured by each FBG strain sensor. In addition, due to the characteristics of the optical signal it can be applied under extreme environments such as long cable lengths and deep seabeds, for example, it is possible to easily measure the position and posture, even in submarine cables or pipelines installed in the deep seabed.

As mentioned above, although embodiments of the present invention have been described, those skilled in the art may add, change, delete, or add components without departing from the spirit of the present invention described in the claims. The present invention may be modified and changed in various ways, which will also be included within the scope of the present invention.

P: Cable C: Centerline
F1: First FBG Strain Sensor F2: Second FBG Strain Sensor
F3: 3rd FBG strain sensor T1: 1st stress triangle
T2: second stress triangle T3: third stress triangle

Claims (11)

(a) installing at least one FGB strain sensor on the object to be detected, wherein the FGB strain sensor is installed to spirally wound on an outer circumferential surface of the object to be detected;
(b) decomposing the tensile rate measured by the FGB strain sensor into a horizontal tensile rate and a vertical tensile rate;
(c) calculating a strain of the detected object based on the horizontal tension rate and the vertical tension rate;
(d) estimating the profile of the object based on the strain; comprising a three-dimensional position estimation method of the object using the FGB strain sensor. The method according to claim 1,
The detected object,
It has a circular cross section, and is formed extending in the longitudinal direction, the three-dimensional position estimation method of the detected object using the FGB strain sensor. The method according to claim 1,
In the step (a)
The at least one FGB strain sensor includes a plurality,
And the plurality of FGB strain sensors are spirally wound around the detected object at the same pitch or twist rate, respectively. The method of claim 3,
The plurality of FGB strain sensors,
A three-dimensional position estimation method of an object to be detected using an FGB strain sensor, which is symmetrically arranged at regular intervals on a cross section. The method according to claim 1,
In the step (a)
The at least one FGB strain sensor is formed of three strands including the first to third FGB strain sensor, 3D position estimation method of the detected object using the FGB strain sensor. The method according to claim 1,
The step (b)
Set a hypothetical stress triangle with a hypotenuse of a portion of the FGB strain sensor, and according to the deformation characteristic of the stress triangle according to the deformation of the object, the tensile rate measured by the FGB strain sensor is the horizontal tensile rate And a three-dimensional position estimation method of the detected object using the FGB strain sensor, which is decomposed at the vertical tensile rate. The method according to claim 1,
In the step (b)
The tensile modulus measured by the FGB strain sensor is decomposed into the horizontal tensile modulus and the vertical tensile modulus by the following equation.

Where ε _r , ε _g , ε _b are the tensile modulus measured at each FBG strain sensor, e _r , e _g , e _b are the vertical tensile modulus of each FBG strain sensor, η is the horizontal direction of each FBG strain sensor Tensile, l, d and h represent the hypotenuse, base and height of each stress triangle without deformation. The method according to claim 1,
In the step (c)
The strain of the target object may include a bending rate, a twist rate and a bending direction of the target object, and a bending rate and torsion rate of the centerline of the target object. Location estimation method. The method according to claim 8,
The three-dimensional position estimation method of a to-be-detected object using a FGB strain sensor, Comprising: The bending rate, the twist rate, and the bending direction of the to-be-detected body are respectively computed by the following formula.

Where t is the twist rate of the object, t ₀ is the initial twist rate of the FGB strain sensor, η is the horizontal tensile rate, and φ is the bending direction of the object, e _r , e _g , e _b indicates the vertical tensile rate of each FGB strain sensor, κ is the bending rate of the object, e _i is e _r , e _g , e _b selected any one of the values, r _c is the center radius of the FGB strain sensor, θ _i represents any one selected from the center angle of each FGB strain sensor. The method according to claim 8,
The bending rate and torsion rate of the said centerline are respectively derived by the following formula, The three-dimensional position estimation method of a to-be-detected body using an FGB strain sensor.

Where τ is the twist rate of the center line, t is the twist rate of the detected object, φ 'is the rotation rate of the bending angle, κ is the bending rate of the center line, e _i is e _r , e _g , e _b selected any one of the values, r _c is the center radius of the FGB strain sensor, θ _i represents any one selected from the center angle of each FGB strain sensor. The method according to claim 1,
The step (d)
A unit tangent vector, a unit normal vector, and a unit vertical vector are calculated through a Fresne-Serre formula, and the calculated unit tangent vector is integrated in the longitudinal direction as shown in the following formula to estimate the profile of the object centerline. 3. A method of estimating a three-dimensional position of an object to be detected using an FGB strain sensor, comprising a step.

Wherein T represents the unit tangent vector.

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