WO2023021619A1 - 統合化iga-dfosシステム - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
- G01D5/26—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
- G01D5/32—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light
- G01D5/34—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells
- G01D5/353—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre
- G01D5/35338—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre using other arrangements than interferometer arrangements
- G01D5/35354—Sensor working in reflection
- G01D5/35358—Sensor working in reflection using backscattering to detect the measured quantity
- G01D5/35361—Sensor working in reflection using backscattering to detect the measured quantity using elastic backscattering to detect the measured quantity, e.g. using Rayleigh backscattering
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
- G01B11/18—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge using photoelastic elements
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L1/00—Measuring force or stress, in general
- G01L1/24—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet
- G01L1/242—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet the material being an optical fibre
Definitions
- This application relates to the integrated IGA-DFOS system.
- DFOS Distributed Fiber Optic Sensing
- DFOS Distributed Fiber Optic Sensing
- Typical methods of this distributed optical fiber sensing technology include Raman, Brillouin, and Rayleigh methods.
- the degree of freedom of the space as a passage for laying the optical fiber has been limited due to restrictions such as the connection of the optical fiber and the space provided (see Patent Documents 1-2 and Non-Patent Documents 1-6). ).
- BEM boundary element method
- K. Nishiguchi, et al. Error analysis for 3D shape sensing by fiber-optic distributed sensors”, Proceedings of the 49th ISCIE International Symposium on Stochastic Systems Theory and Its Applications, Hiroshima, Nov.3-4, 2017 Y.
- Kishida, et al., Study of Optical Fibers Strain-Temperature Sensitivities Using Hybrid Brillouin-Rayleigh System”, PHOTONIC SENSORS/Vol.4, No.1, 2014:1-11, DOI:10.1007/s13320-013- 0136-1 Y. Yamauchi, et al., ”A STUDY OF THE STABILITY, RELIABILITY, AND ACCURACY OF NEUBRESCOPE-BASED PIPE THINNING DETECTION SYSTEM”, The 3rd International Conference on Structual Health Monitoring of Intelligent Infrastructure, Vancouver, British Columbia, Canada, Nov. 13-16, 2007
- load conditions, boundary conditions, and defects or deterioration of structures are input as known information, and safety evaluation is performed (forward analysis technology).
- general analysis technology back analysis technology for reverse analysis of load conditions, boundary conditions, defects, deterioration, etc. based on monitored partial information has not been established.
- FO installation plan (a plan to facilitate installation such as FO installation route), countermeasures against risk factors that are concerns of CAD design data, evaluated load and operating environment conditions, corrosion or earthquake, etc.
- the purpose is to reflect the impact of
- the DFOS measurement system which is a highly accurate and reliable distribution measurement system for the strain and temperature of the object to be measured
- the IGA numerical analysis model hereafter, this numerical analysis model is called " Fiber mesh embedded type IGA analysis model”
- Fiber mesh embedded type IGA analysis model is applied to immediately measure the deformation of the object to be measured, and by remotely monitoring the load status, the object, including the part where the FO is not installed.
- the integrated IGA-DFOS system disclosed herein comprises: an optical fiber attached to an object to be measured and sensing a physical quantity of the object to be measured; a distribution calculation type optical fiber measurement device that calculates a physical quantity of the object to be measured based on the sensing signal detected by the optical fiber and obtains a distribution state of the physical quantity; a fiber mesh embedded IGA analysis tool that incorporates a fiber mesh that is modeled with non-uniform rational B-spline basis functions and that forms the shape of the optical fiber; with The distribution state of the physical quantity of the object to be measured at the mounting position of the optical fiber measured by the distribution calculation type optical fiber measuring device is input to the fiber mesh built-in IGA analysis tool, and the optical fiber is mounted. Obtaining the distribution state of physical quantities of the object to be measured other than the position, It is characterized by
- the integrated IGA-DFOS system disclosed in the present application, countermeasures against risk factors that are concerns of CAD design data are added to the FO installation plan (a plan for facilitating installation, such as the installation route of the FO) , the evaluated load and environmental conditions of use, the effects of corrosion or earthquakes, etc. can be reflected.
- FO installation plan a plan for facilitating installation, such as the installation route of the FO
- FIG. 1 is a block diagram for explaining the configuration of an integrated IGA-DFOS system according to Embodiment 1;
- FIG. FIG. 4 is a diagram showing an example of a two-dimensional NURBS curve in the integrated IGA-DFOS system of Embodiment 1; 4 is a diagram for explaining moving average fiber distortion in the integrated IGA-DFOS system of Embodiment 1;
- FIG. 4 is a diagram for explaining the flow of elastic stress analysis and fiber strain calculation at all sampling points in the IGA numerical analysis model relating to the integrated IGA-DFOS system of Embodiment 1;
- FIG. 5 is a diagram showing an experimental model for explaining an application example of the formulation proposed in the IGA numerical analysis model related to the integrated IGA-DFOS system of Embodiment 1; 6 is a diagram showing the relationship between the maximum strain value of the optical fiber and the displacement value of the cylindrical pipe in the experimental model of FIG. 5.
- FIG. It is a figure which shows the relationship between the simulation result of the strain distribution of the optical fiber using the said IGA numerical analysis model, and the experimental data obtained with the experimental model. It is a figure for demonstrating the load along a cylindrical pipe as an example about the reverse IGA method in the said IGA numerical analysis model. It is a figure which shows the simulation result of the pressure distribution of the cylindrical pipe longitudinal direction optimized by the said IGA numerical analysis model.
- FIG. 4 is a diagram showing the relationship between the simulation result of fiber strain optimized by the IGA numerical analysis model and the experimental data obtained by the experimental model. It is the table
- FIG. 1 is a block diagram for explaining the configuration of an integrated IGA-DFOS system according to Embodiment 1, which has been newly developed to solve the above problems.
- the solid-line arrows are items related to the contents constituting the integrated IGA-DFOS system of the first embodiment, and the dotted-line arrows show the ripple effect of the integrated IGA-DFOS system of the first embodiment.
- NURBS Non-Uniform Rational B- An abbreviation for Spline, an IGA (Isogeometric Analysis) numerical analysis model including a non-uniform rational B-spline model and an FO mesh that fuses FO (optical fiber) laying plans has been newly developed.
- the FO installation plan (a plan for facilitating mounting (installation), such as the installation route of the FO) includes countermeasures and evaluation of risk factors that are concerns of CAD design data. It is now possible to reflect the applied load and operating environmental conditions, as well as the effects of corrosion and earthquakes.
- this development has realized a DFOS measurement system, which is a highly accurate and reliable distribution measurement system for strain, temperature, etc. of the object to be measured, and the FO mesh can
- this numerical analysis model is also called "fiber mesh embedded IGA analysis model”
- real-time measurement of the deformation of the object to be measured and the load status can be calculated. It became possible to monitor remotely, and based on this, it became possible to reverse analyze the deformation and load (in-plane load and out-of-plane load) of the object to be measured, including parts where FO is not installed. .
- the above-mentioned FO mesh is modeled with the NURBS basis/shape function. Since the mesh can be easily created by simple input from CAD to the IGA system, integration, efficiency, and industrialization of the measurement and monitoring target system can be achieved.
- the integrated IGA-DFOS system of Embodiment 1 consists of two main components, a part related to FO sensing technology and a part related to fiber mesh embedded IGA analysis technology.
- the former FO sensing technology has the advantage that the data it acquires is realistic and can capture the partial phenomenon of the object to be measured, but it also has the problem that the essence of the phenomenon may not be directly reflected.
- the latter fiber mesh embedded IGA analysis technology is based on theory and has the advantage of being able to capture the entire inside and outside of the object to be measured. It also has the potential to clarify the nature of phenomena.
- the IGA tool is used to include DFOS information based on the proposal of the optical fiber mesh model (hereinafter simply referred to as the fiber mesh model).
- the analytical model used in the IGA tool can be obtained directly from CAD (using the basis functions used in CAD as shape functions) and the initial and boundary conditions can be obtained directly or indirectly from DFOS in real-time and remotely. can provide.
- Fiber optic sensors can perform distribution measurements with a single fiber without multiplexing sensors.
- TW-COTDR Rayleigh frequency shift
- the method using Rayleigh frequency shift called TW-COTDR is based on the Rayleigh backscattering phenomenon, which is elastic scattering (random refractive index variation along the fiber that occurs when light passes through an optical fiber). ), and changes in strain or temperature cause this Rayleigh frequency shift.
- the strain or temperature of interest is then determined by comparing the frequency difference measured between the base and reference conditions via cross-correlation. This method achieves high resolution (cm order) and stable accuracy (less than 0.1 ⁇ ).
- the coordinate system in IGA will be described.
- the first space is the Gaussian space (range: -1 to 1) in which the Gaussian integration points are defined.
- the second space is the parametric space in which the basis functions are evaluated. In IGA terminology, it also represents the parent element of the NURBS shape and the normalized knot vector.
- the second space is the physical space in which the shape itself exists.
- Equation (2) is the Jacobian from parametric space to Gaussian space.
- the parametric curve c( ⁇ ) is defined by the product of the univariate basis functions N i and the control point coordinates C i (equation (3)).
- the same criteria can be used to represent fields such as displacement or strain.
- the control point coordinates C i are replaced by the control parameters.
- the displacement field is represented by equation (4)
- the Jacobian from physical space to parametric space is represented by equations (5) to (7).
- Basis functions are an important part of single-parameter formulation and single-shape analysis, as they are used to represent both the shape field and the solution field.
- a univariate B-spline basis function of order p is defined by the Cox-de Boor recursion (see equation (8)).
- the knot vector is the set of non-decreasing real numbers in the parametric space. Note that the first and last control points match the physical geometry. Also, normalized knots always between 0 and 1 are used.
- NURBS basis functions are formed by projective transformation of B-splines to allow accurate representation of conic sections.
- a univariate NURBS basis is defined by equation (9).
- the trivariate NURBS basis functions are defined in equation (10) as the tensor product of the univariate B-spline basis functions and their respective weights.
- weight values are assigned to control points and called during basis function evaluation.
- the first derivative of the B-spline basis function is defined by equation (11).
- the first derivative of the NURBS basis functions is defined in equation (12). Derivatives with respect to physical functions can be obtained using the Jacobian (see equation (13)).
- NURBS basis functions have the following properties. a) non-negative; b) unity partitioning (basis functions sum to unity); c) locality (the support or influence of the basis functions only over a limited area within the shape); d) Convex hull (the shape is always inside the control polygon). e) Affine covariance (that the shape is transformed in the same way as the control points).
- Implicit elastic IGA is similar to conventional FEM, except that it uses basis functions and connectivity, and control points instead of nodal points. In this section, we briefly describe the linear IGA formulation of the solid structure.
- B is a strain-displacement matrix and is represented by Equation (16).
- the stress ⁇ can be derived from the relationship between strain and constituent elements in each term of the material matrix D (equation (17)).
- the potential energy is Eq. (18) and the minimum energy steady state can be obtained as Eqs. (19) and (20) using the derivative with respect to the discretized displacement.
- Equations (21) and (22) Equations (21) and (22).
- optical fiber mesh optical fiber mesh
- the shape of an optical fiber can be represented as a univariate parametric NURBS curve in three dimensions, assuming that the mass and stiffness of the optical fiber contribute little to the structural system being measured.
- the parametric fiber coordinate as ⁇
- the physical coordinate x also called global coordinate x in the following
- the one-dimensional physical fiber coordinates can then be viewed as the arc length s( ⁇ ) of the curve derived from equation (26).
- FIG. 2 shows an example of a second-order two-dimensional NURBS curve. In FIG. 2, four control points (C 1 to C 4 ) and a tangent vector t are shown.
- the fiber strain is not a single-point strain, but is averaged over the distance d (hereafter also referred to as length d) between the points of the two black dots, as shown in FIG.
- the moving average fiber strain over d (same as the average moving window) is given by equations (31) and (32).
- b is the sampling interval
- the length d is also the sampling resolution.
- Fig. 4 shows a flow chart summarizing elastic stress analysis and fiber strain calculation at all sampling points.
- IGA makes structural and fiber optic CAD data available in the form of NURBS control points and knot vectors for streamlined CAE workflow.
- Existing simple geometric algorithms can also be implemented in the analysis code to perform efficient and accurate calculations.
- DFOS can provide distributed strain data with a simple setup, has high spatial resolution, long range (25 km), and 24/7 remote monitoring capabilities.
- Rayleigh backscatter sensors have higher spatial resolution than FBG (Fiber Bragg grating) sensors.
- the fiber mesh is independent of the type of fiber strain sensor as only fiber geometry and measurement information is required as input. Using fiber meshes and inverse analysis techniques (discussed in detail below), real-time structural states such as deformations, loads, stresses, and strain distributions can be inferred from observed fiber strain data.
- the continuity of the displacement field (indicated by the symbol C0, the same applies hereinafter) is guaranteed, but the continuity of the tangent line (C1) is not guaranteed (see FIG. 2.
- the given points are the four points C 1 , C 2 , C 3 and C 4 shown in FIG. 2, and the continuity of the displacement field is realized at these four points. (implemented by the straight lines between points C1 and C2 , between points C2 and C3 , and between points C3 and C4 shown in FIG. 2), between points C1 and C4
- a seamless analysis model can be constructed by establishing a unified realization method using a CAD tool that includes an analysis model. From real-time long-distance measurement information by optical fiber, it is possible to analyze deformation and load information that cannot be theoretically predicted, such as the inside of the monitored object where the optical fiber is not laid directly, or contact. By collecting time transition data of the monitored object, it is possible to estimate the change or remaining life of the monitored object. It is possible to update the improvement effect of repairing the monitored object and the information change of the object of interest due to unexpected events such as earthquakes.
- FIGS. 5A and 5B show schematic diagrams of the experimental apparatus tested.
- a threaded rod 2 having a length corresponding to the diameter of the cylinder is installed at the center of the inner circumference of a vinyl chloride cylindrical pipe 1, and the outer circumference of the cylinder is protected with tape.
- the optical fiber 3 is spirally wound four times at a pitch lp of 33 mm.
- the coordinate positions (fiber coordinates) on the cylindrical surface of this optical fiber are marked for later use in the simulation. Both ends of the optical fiber are connected to an input terminal and an output terminal of the distribution computing type optical fiber measuring device 4, respectively.
- a load is applied to the cylindrical pipe 1 by rotating the threaded rod 2 installed in the central portion of the cylindrical pipe 1 (diameter position of the cylindrical pipe).
- the load is distributed in the longitudinal direction of the pipe by a pair of rectangular beams 5 provided on the inner peripheral portion of the cylindrical pipe.
- two dial gauges 6 provided on the outer peripheral portion of the cylindrical pipe 1 corresponding to the installation position of the threaded rod 2 measure the total displacement caused by the load.
- the strain distributed in the cylinder (DFOS strain) is measured by the sample distribution calculation type optical fiber measuring device 4 that uses Rayleigh backscattered light that is accurate and has excellent spatial resolution.
- the TW-COTDR measurement mode was used to measure the strain of the optical fiber at 1 cm intervals.
- the reference strain distribution under the minimum deformation of the pipe is obtained.
- the threaded rod 2 is rotated to apply a constant amount (one stroke) of displacement. Net displacement is calculated as the average of the two dial gauge readings.
- the displacement deforms the cylindrical pipe into an elliptical shape and is detected as 1D (one-dimensional) strain by the optical fiber.
- the measured strain is subtracted by the reference strain value to obtain the true value.
- the stroke is increased and the process is repeated to obtain the fiber strain for all load cases.
- the strain of the optical fiber Since the cylindrical pipe deforms into an elliptical shape, the strain of the optical fiber has a waveform that oscillates between a positive value (tensile strain) and a negative value (compressive strain) with respect to the fiber coordinates. Therefore, the maximum strain value of the optical fiber and the displacement value of the cylindrical pipe are plotted for the strain of the optical fiber with respect to the deformation of the cylindrical pipe, and are shown in FIG. From FIG. 6, it can be said that the strain of the optical fiber changes linearly with respect to the displacement value of the cylindrical pipe. From this, it can be said that the linear model may be used in the numerical analysis simulation.
- the NURBS geometry of the cylindrical pipe under test was created using a trivariate quadratic function and 81 control points to accurately represent the hollow cylinder.
- three C0 continuous lines are introduced along the circumference and the basis functions are C1 continuous everywhere else, suitable for analysis.
- FIG. 7A shows a superimposed graph of the simulated and experimental data for the strain distribution of the fiber for load case 3 (Case M3).
- FIG. 7B shows the corresponding positions on the cylinder of the coordinates AE shown in FIG. 7A. From this FIG. 7A, it can be seen that the trends of the simulation results closely follow the experimental data, except for the peak values.
- the above boundary conditions can be estimated by minimizing the error between the observed and simulated fiber strains using an optimization approach.
- This approach of estimating the unknown variable, the boundary condition, from the known experimental data, the fiber strain, is called inverse IGA.
- the estimated boundary conditions can then be used in forward simulations to obtain the displacement and stress distributions.
- the unknown load along the cylindrical pipe is defined as the pressure distribution over the surface area of the cylindrical pipe in contact with the rectangular bar (see Figure 8A).
- the change in pressure along the length direction (Z direction) of the cylindrical pipe is represented by a quadratic B-spline function with five coefficients as parameters, as shown in FIG. 8B.
- the objective function E is defined as the sum of the squared errors between the observed and calculated fiber strains at each sampling point along the fiber ( See formula (33)).
- ⁇ f refers to the moving average fiber strain defined in Eq. (31).
- the objective function E is minimized with respect to the optimization parameters p i of the pressure distribution function of FIG. 8B and least squared to obtain the optimal solution.
- the optimization termination criterion is that ⁇ E, which is the value of the difference between successive iterations, is less than 10 ⁇ 4 ⁇ .
- FIG. 9 shows the results of optimized pressure distribution with input fiber strain from load case 3 . From this figure, it can be seen that the pressure distribution is not constant, and the pressure in the central portion of the pipe is high.
- Fig. 10 shows the optimized fiber strain simulation results. From this figure, it can be seen that the difference between the simulation results and the experimental data is smaller than in the case of FIG. 7, and the degree of matching between the two is higher.
- FIG. 11 shows the result of numerically evaluating the effect of the reverse IGA method. From this table, it can be seen that both the root mean square and the maximum deviation of the optical fiber strain error in the inverse IGA method are about 1/2 of those in the forward analysis method, indicating that the inverse IGA method is effective. It turns out that It should be noted that the reverse IGA method described above is applicable not only to the strain measuring optical fiber, but also to analysis of observation data in combination with other sensors such as a pressure sensor or a temperature sensor.
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Description
a)対象となる形状を有限要素によりモデル化する際、メッシュ生成が必須であることなどにより、長い作業時間とコストがかかる。
b)境界条件、あるいは負荷条件は、理想化して定められることが多いため、実際の条件とは異なる。
c)腐食、あるいは欠陥による形状、又は材料特性が変化した場合、それらを反映させたモデルの再構築が必要となるため、実際の使用においては現実的ではない。
a)図面設計をベースに建造した構造物は、その使用中に劣化し、本来の理想的な構造物ではなく、欠陥のある構造物となっている。このような欠陥などの存在する実際の構造物のライフサイクルを監視する現状の手法は、モニタリング精度、あるいは使用の自由度が不十分である。
b)現状、欠陥、あるいは劣化のある実際の構造物の破損、破壊プロセスなどに対して適用されるコアモニタリング技術、情報収集力は非常に不足している。
c)自動車、あるいは電子部品などの量産品に対する数値解析は日常的に行われているが、個別仕様で製造される構造体を対象とする数値解析に対しては、明確なガイドラインがなく、モニタリング手法も定まっていない。
d)現状の数値解析技術では、構造体の負荷条件、境界条件、および欠陥、あるいは劣化を既知の情報として入力し、安全性評価を行っている(順解析技術)。一方、モニタリングした部分的な情報を基に、負荷条件、境界条件、及び欠陥、あるいは劣化などを逆解析する一般的な解析技術(逆解析技術)は、確立されていない。
被測定体に装着されて前記被測定体の物理量をセンシングする光ファイバと、
前記光ファイバで検出されたセンシング信号を基に前記被測定体の物理量を演算し、当該物理量の分布状態を求める分布演算型光ファイバ計測装置と、
非一様有理Bスプライン基底関数でモデル化され、前記光ファイバの形状を形成するファイバメッシュを組み込んだファイバメッシュ組込型IGA解析ツールと、
を備え、
前記分布演算型光ファイバ計測装置により計測された、前記光ファイバの装着位置での被測定体の物理量の分布状態を、前記ファイバメッシュ組込型IGA解析ツールに入力して、前記光ファイバの装着位置以外での被測定体の物理量の分布状態を求める、
ことを特徴とするものである。
[統合化IGA-DFOSシステムの概要]
実施の形態1の統合化IGA-DFOSシステムについて、以下図を用いて説明する。
図1は、上述の課題を解決するために新たに開発された実施の形態1の統合化IGA-DFOSシステムの構成を説明するためのブロック図である。図中、実線の矢印は、実施の形態1の統合化IGA-DFOSシステムを構成する内容に関わる項目であり、点線の矢印は実施の形態1の統合化IGA-DFOSシステムの波及効果を示している。
はじめに、実施の形態1の統合化IGA-DFOSシステムの主要構成要素の詳細について説明する。実施の形態1の統合化IGA-DFOSシステムは、2つの主要構成部分である、FOセンシング技術に関わる部分と、ファイバメッシュ組込型IGA解析技術に関わる部分とで構成されている。
光ファイバセンサは、センサを多重化することなく、単一のファイバにより分布測定を実行できる。特に、歪の計測に用いられるTW-COTDRと呼ぶレイリー周波数シフトを利用する方式は、弾性散乱であるレイリー後方散乱現象(光が光ファイバを通過するときに生ずるファイバに沿ったランダムな屈折率変動による)を用いた方式であり、歪あるいは温度の変化がこのレイリー周波数シフトを引き起こす。そこで、相互相関を介して基準状態と参照状態との間で測定された周波数差を比較することにより、目的とするひずみ、あるいは温度を求める。なお、この方式では、高い分解能(cmオーダー)と安定した精度(0.1με未満)を実現している。
まず、IGAにおける座標系について説明する。IGAのような、単一パラメータ定式化では、主に、3つの座標系(空間)がある。1番目の空間は、ガウス積分点が定義されているガウス空間(範囲:-1~1)である。2番目の空間は、基底関数が評価されるパラメトリック空間である。IGAの用語では、NURBS形状の親要素と正規化ノットベクトルも表わす。2番目の空間は形状自体が存在する物理空間である。
基底関数は、形状の場と解の場の両方を表すために使用されるので、単一パラメータ定式化と、単一形状分析の重要な部分である。次数pの単変量Bスプライン基底関数は、Cox-de Boor再帰式によって定義される(式(8)参照)。
a)非負性。
b)単一性の分割(基底関数の合計が1になること)。
c)局所性(基底関数のサポートまたは影響が形状内の限られた領域にのみ及ぶこと)。
d)凸包(形状が常に制御多角形の内側にあること)。
e)アフィン共分散(形状が制御点と同じ方法で変換されること)。
黙示的な弾性IGAは、基底関数と接続性、およびノードポイントの代わりに制御点を使用することを除いて、従来のFEMと同様である。本節では、固体構造の線形IGA定式化について簡単に説明する。
光ファイバの形状は、光ファイバの質量と剛性が計測対象である構造システムにほとんど寄与しないと仮定して、3次元での単変量パラメトリックNURBS曲線として表すことができる。パラメトリックファイバ座標をξとして設定すると、物理座標x(以下ではグローバル座標xとも呼ぶ)はξの関数として式(25)から計算できる。そうすると、1次元の物理的なファイバ座標は、式(26)から導き出される曲線の弧長s(ξ)とみなせる。
式(24)の連立方程式を解くことにより、ファイバのひずみ分布は式(15)から求められる。1次元のファイバひずみを計算するため、ファイバが取付られた構造の表面のひずみテンソルをファイバのサンプリングポイントでの接線ベクトルとともに使用する。グローバル座標xに対応するサンプリングポイントSでの1次元ファイバひずみは、ファイバの接線方向にひずみテンソルを投影して計算できる(式(29)、式(30)参照)。
統合されたIGAおよびDFOSの定式化の主な利点は、以下の通りである。
IGAでは、効率化されたCAE業務の流れのために、構造および光ファイバのCADデータをNURBS制御点およびノットベクトルの形式で使用できる。既存の簡潔な幾何学的アルゴリズムを分析コードに実装して効率的かつ正確な計算を行うこともできる。さらに、IGAの総自由度の観点から、解析メッシュサイズに関係なく、正確な形状を表現する能力と高効率が多くの研究者によって検証されている。
光ファイバの線上における(部分的な)分布型の計測された歪を、ファイバメッシュ組込型IGA解析モデルに入力して、全体現象を順解析する技術を開発した。なお、従来、光ファイバによって計測されたデータは、理論的な数値解析結果を検証するためだけに利用されていた。
ファイバメッシュ組込型IGA解析に必要な負荷条件、境界条件、および欠陥・材料の劣化を未知数として設定して、分布型の計測された歪に合致するように、逆解析する技術の開発(DFOSひずみデータから未知の境界条件などを推定)。
ファイバメッシュ組込型IGA解析ツールは、変位場の接続連続性(記号C1で示す。以下同様)の技術を利用するため、光ファイバの敷設特性の1つである接線の連続性(C1)と合致しており、要素技術としての精度保証がなされる。なお、従来の有限要素法では、変位場の連続性(記号C0で示す。以下同様)は保証されているが、接線の連続性(C1)は保証されていない(図2参照。ここで、従来の有限要素法では、与えられる点は図2に示す点C1、点C2、点C3、点C4の4点であり、変位場の連続性は、これら4点で実現されるが(図2に示す、点C1と点C2間、点C2と点C3間、点C3と点C4間の直線で実現される)、点C1と点C4間を結ぶ曲線は、元元与えられていない。一方、新たに開発したファイバメッシュ組込型IGA解析モデルでは、図2中の点C1と点C4間を結ぶ曲線がNURBSモデルにより与えられるため(NURBSモデルでは、点C1、点C2、点C3、点C4は制御点とも呼ばれる)、この曲線の点C1と点C4間での任意の点での接線が存在する(図2中、代表点での接線ベクトルtを参照)。つまり、接線の連続性を有している。このため、与えるべき点は最少、点C1と点C4だけで済むため、点の設定時間が有限要素法に比べて短縮される)。
設計段階からの光ファイバの敷設法に関して、解析モデルを含むCADツールによる一元化された実現手法を確立したことで、シームレスな解析モデルを構築することができる。
リアルタイムの光ファイバによる遠距離計測情報から、光ファイバが直接、敷設されていない監視対象の内部、あるいは接触など理論予測できない変形・荷重の情報を解析することができる。
監視対象物の時間推移データを収集することにより、監視対象物の変化、あるいは余寿命の推測が可能である。
監視対象物の補修による改善効果、地震などの意外イベントによる関心対象物の情報変化をアップデートできる。
次に、弾性応力・ひずみ解析について、統合されたIGAとDFOSを使用した、上記提案の定式化の適用例を、円筒パイプを用いた実験モデルにより説明する。
開発した手法を検証するため、外径300mm、長さ254mmで肉厚5mmの塩化ビニル製の円筒パイプ(ヤング率:2.8GPa、ポアソン比0.38)に変形を生じさせ、発生する歪を計測する実験を行った。この実験に用いた実験装置について、まず説明する。
実験は、円筒パイプの変形に対する光ファイバ歪の応答を確認するため、M1からM5と名付けられた5つの変位のケースに対して実行された。具体的な変位の値は、M1:172μm、M2:308μm、M3:534μm、M4:755μm、M5:887μm、である。また、実験のパラメータとしてのファイバ歪のサンプリング間隔は1cm、ファイバ歪測定の移動平均距離で定義される空間分解能は2cm、歪の再現性は±1μεである。
円筒パイプが楕円形に変形するため、光ファイバの歪は、ファイバ座標に対して、正の値(引張ひずみ)と負の値(圧縮ひずみ)の間を振動する波形となった。そこで、円筒パイプの変形の大きさに対する光ファイバ歪について、光ファイバの最大ひずみの値と円筒パイプの変位値をプロットし、図6に示す。図6より、光ファイバの歪は円筒パイプの変位値に対して線形に変化しているといえる。これより、数値解析シミュレーションで線形モデルを使用してよいと言える。
円筒パイプと光ファイバのモデルを単純な境界条件を用いて順IGAでシミュレーションし、シミュレーション結果を実験データと比較する。
供試の円筒パイプのNURBS形状は、3変量の2次関数と81個の制御点を使用して作成され、中空の円筒を正確に表現した。この標準構造では、円周に沿って3本のC0連続線が導入され、基底関数は、他の全ての箇所でC1連続であり、解析に適している。
さらに、付随するファイバ形状として、単変量の2次関数と33個の制御点を使用して螺旋曲線が作成された。
図7Aに、荷重ケース3(ケースM3)の場合の、ファイバの歪分布のシミュレーション結果と実験データを重畳したグラフを示す。図7Bに、図7A中に示した座標A~Eの円筒状での対応する位置を示した。この図7Aから、シミュレーション結果の傾向は、ピーク値を除き、実験データに厳密に従っていることがわかる。
上記4.3節では、シミュレーションが、引張側のファイバひずみを過大に予測した。シミュレーションの値と実験データの不一致は、これらの間での異なる境界条件に起因する可能性があることを前節で指摘した。実際の現場においては、境界条件が不明な場合がよくある。一方で、荷重は、構造と安全性を決定するための重要なパラメータであることから、利用可能なファイバ歪データから境界条件を推定する数値的手法は有益であると思われる。そこで、この手法について以下説明する。
なお、上述の逆IGA法は、歪測定用光ファイバだけではなく、他のセンサである圧力センサ、あるいは温度センサとの組合せによる観測データの解析にも同様に適用可能である。
従って、例示されていない無数の変形例が、本願明細書に開示される技術の範囲内において想定される。例えば、少なくとも1つの構成要素を変形する場合、追加する場合または省略する場合が含まれるものとする。具体的には、非一様有理Bスプライン基底関数でのモデル化はCADツールを用いて作成されることを前提として説明したが、設計段階からの光ファイバの敷設法に関して、解析モデルを含む別のツールにより一元化された手法であって、シームレスな解析モデルを構築することができるものであれば、CADツールに限るものではない。
Claims (5)
- 被測定体に装着されて前記被測定体の物理量をセンシングする光ファイバと、
前記光ファイバで検出されたセンシング信号を基に前記被測定体の物理量を演算し、当該物理量の分布状態を求める分布演算型光ファイバ計測装置と、
非一様有理Bスプライン基底関数でモデル化され、前記光ファイバの形状を形成するファイバメッシュを組み込んだファイバメッシュ組込型IGA解析ツールと、
を備え、
前記分布演算型光ファイバ計測装置により計測された、前記光ファイバの装着位置での被測定体の物理量の分布状態を、前記ファイバメッシュ組込型IGA解析ツールに入力して、前記光ファイバの装着位置以外での被測定体の物理量の分布状態を求める、
ことを特徴とする統合化IGA-DFOSシステム。 - 前記非一様有理Bスプライン基底関数でのモデル化は、CADツールを用いて作成されることを特徴とする請求項1に記載の統合化IGA-DFOSシステム。
- 前記光ファイバの装着位置以外での被測定体の物理量の分布状態を求める際の負荷条件、境界条件、および材料の欠陥あるいは劣化の値は、予め与えられた値を用いることを特徴とする請求項1または請求項2に記載の統合化IGA-DFOSシステム。
- 前記ファイバメッシュ組込型IGA解析ツールで解析を行う際の、負荷条件、境界条件、および材料の欠陥あるいは劣化の値を未知数として設定して、前記分布演算型光ファイバ計測装置で求められた物理量の分布状態に合致するように、前記ファイバメッシュ組込型IGA解析ツールを用いて、未知数である前記負荷条件、境界条件、および材料の欠陥あるいは劣化の値を、既定の推測法により推測して求め、この求められた推測値を用いて前記被測定体の物理量の分布状態を解析して求めることを特徴とする請求項1または請求項2に記載の統合化IGA-DFOSシステム。
- 前記ファイバメッシュ組込型IGA解析ツールの前記非一様有理Bスプライン基底関数は、前記被測定体の位置に関する連続性、および当該位置の変化に関する連続性を有していることを特徴とする請求項1から4のいずれか1項に記載の統合化IGA-DFOSシステム。
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