Apparatus and method for calculating the behavior of linear structures

Abstract

The objective of the present disclosure is to enable the behavior of a linear structure in water to be estimated.　The present disclosure provides a device which: represents at least one parameter using a plurality of discrete values; estimates the behavior of a linear structure using each of the discrete values; acquires the behavior of the linear structure as detected using an optical fiber; calculates the likelihood of the predicted behavior of the linear structure and the acquired behavior of the linear structure; updates at least any one of the plurality of discrete values on the basis of the likelihood; and uses the updated plurality of discrete values to calculate the behavior of the linear structure.

Description

[Technical field]

[0001] The present disclosure relates to an apparatus and method for estimating the behavior of an underwater linear structure, such as a submarine cable, by using reflectometry technology with optical fibers. [Background technology]

[0002] A method has been proposed to detect the behavior of underwater linear structures such as submarine cables using optical fiber sensors. Optical fiber sensors are a technology that measures and analyzes the reflection spectrum of optical fiber using OFDR (Optical Frequency Domain Reflectometry) to derive the three-dimensional shape of the object being measured. Optical fiber sensors are capable of dynamic measurement over long distances. However, monitoring of underwater linear structures has a problem of error accumulation due to integral calculations along the optical fiber.

[0003] Also, as a method suitable for estimating phenomena in real time, there is an example of behavior estimation by sequential data assimilation, in which data assimilation is performed each time observation data is obtained (for example, see Non-Patent Document 1). However, this method uses discrete position information of linear structures obtained from the Global Positioning System (GPS) or the like as observation data. In order to obtain position information, it is necessary to receive radio waves underwater. For this reason, as the underwater depth increases, it becomes difficult to obtain position information, and there is a problem that it is difficult to obtain continuous data in the length direction. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] JV Grindheim, I. Revahug, and E. Pedersen, “Utilizing the ensemble kalman filter and ensemble kalman smoother for combined state and parameter estimation of a three dimensional towed underwater cable model”, Journal of Offshore Mechanics and Arctic Engineering, Vol.139, No.6, p.061303, 2017. Summary of the Invention [Problem to be solved by the invention]

[0005] The present disclosure aims to make it possible to estimate the behavior of a linear structure underwater. [Means for solving the problem]

[0006] The apparatus and method according to the present disclosure include: expressing at least one parameter as a plurality of discrete values, and predicting the behavior of the linear structure using each of the discrete values; Obtaining the behavior of the linear structure detected using an optical fiber; Calculating a likelihood between the predicted behavior of the linear structure and the acquired behavior of the linear structure; updating at least one of the plurality of discrete values ​​based on the likelihood; The behavior of the linear structure is calculated using the updated discrete values. Effect of the Invention

[0007] The present disclosure makes it possible to estimate the behavior of a linear structure in water. [Brief description of the drawings]

[0008] [Figure 1] 1 illustrates an example of a system configuration according to the present disclosure. [Diagram 2] 2 illustrates an example of a hardware configuration of an apparatus according to the present disclosure. [Diagram 3] An example of the deformation image of two cores is shown. [Figure 4] An example of the displacement in the rotational direction is shown. [Diagram 5] 1 shows an example of a flow chart illustrating the method of the present disclosure. [Figure 6] 4 shows the results of estimating the behavior of a linear structure when the present disclosure is not used. [Figure 7] 13 shows the results of estimating the behavior of a linear structure when the present disclosure is used. [Figure 8] 1 illustrates an example of a system configuration according to the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, the embodiments of the present disclosure will be described in detail with reference to the drawings. Note that the present disclosure is not limited to the embodiments shown below. These implementation examples are merely illustrative, and the present disclosure can be implemented in various forms with various modifications and improvements based on the knowledge of those skilled in the art. Note that components with the same reference numerals in this specification and drawings are assumed to indicate the same components.

[0010] (Embodiment 1) An example of the system configuration of this embodiment is shown in Fig. 1. In the system of this embodiment, an apparatus 10 is mounted on a ship 100, and the apparatus 10 is connected to a linear structure 20. The apparatus 10 of this embodiment is an apparatus for calculating the behavior of a linear structure of the present disclosure, and estimates the behavior of the linear structure 20 existing in water by parameter estimation through distributed optical fiber sensors and data assimilation based on Bayesian inference.

[0011] The behavior of the linear structure 20 is, for example, the three-dimensional coordinates of the linear structure 20. The three-dimensional coordinates of the linear structure 20 can be calculated using the displacement in the rotational direction of the linear structure 20 with respect to the position of at least one point of the linear structure 20 for which position information can be acquired. Therefore, in this embodiment, an example will be described in which the behavior of the linear structure 20 is the displacement in the rotational direction for each length L of the linear structure 20.

[0012] 2 shows an example of a hardware configuration of the device 10. The device 10 of this embodiment includes an information processing unit 11, a storage unit 12, an optical fiber sensor 13, and an input unit 14. The input unit 14 is any means capable of inputting parameters, such as a keyboard or a touch panel. The optical fiber sensor 13 is connected to optical fibers 21 and 22 arranged along a linear structure 20.

[0013] The optical fiber sensor 13 detects strains ε1 and ε2 in the two optical fibers 21 and 22. An optical fiber sensor using a Brillouin Optical Time Domain Reflectometer (BOTDR) can be exemplified as a means for detecting strain in the optical fibers 21 and 22. The following description will be given assuming that the optical fiber sensor 13 is a BOTDR.

[0014] The information processing unit 11 calculates the behavior of the linear structure 20 by using the distortion detected by the optical fiber sensor 13. The displacement in the rotational direction of the linear structure 20 can be obtained by using the length L of the linear structure 20 and the deflection angle θ [rad] at the length L of the linear structure 20. Therefore, the information processing unit 11 calculates the deflection angle θ [rad] for each length L of the linear structure 20 by using the distortions ε1 and ε2 of the linear structure 20. An example in which the information processing unit 11 calculates the deflection angle θ [rad] for each length L of the linear structure 20 as the behavior of the linear structure 20 will be described below.

[0015] Furthermore, the information processing unit 11 uses a simulator to predict the behavior of the linear structure 20. For example, the information processing unit 11 uses any parameters to simulate the behavior of the linear structure 20 and calculates a state quantity U(t). The information processing unit 11 uses the state quantity U(t) to calculate the displacement in the rotational direction for each length L of the linear structure 20.

[0016] The memory unit 12 stores the strains ε1 and ε2 detected by the optical fiber sensor 13, as well as any data used in the processing of the information processing unit 11 and the processing results of the information processing unit 11. The data used in the processing of the information processing unit 11 includes a simulation program for predicting the behavior of the linear structure 20 and parameters used in the simulation program. The device 10 of this embodiment can also be realized by a computer and a program, and the program can be recorded on a recording medium or provided via a network. A detailed explanation will be given below.

[0017] Two optical fibers 21, 22 are placed along an underwater linear structure 20, and the cores of the optical fibers 21, 22 deform to fit the shape of the linear structure 20 as shown in Fig. 3, and distortions of ε1 and ε2 are observed by the optical fiber sensor 13. The deflection angle θ [rad] obtained by integrating the curvature of the underwater linear structure 20 over the length L [m] is expressed by equation (1) using the distance d [m] between the cores of the optical fibers 21 and 22.

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[0018] When the length L is a unit length for predicting the behavior of the linear structure 20, the deflection angle θ in formula (1) corresponds to the displacement in the rotational direction obtained as a simulation predicted value. For example, as shown in Fig. 4, the deflection angles θ1 and θ2 in the actual measurement correspond to the deflection angles θ1 and θ2 in the simulation predicted values.

[0019] When the observation data of the strain distribution detected by the optical fiber sensor 13 is converted into deflection angle data y(t) for each length L, equation (2) is derived.

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[0020] Here, H is an observation matrix that extracts the rotational displacement of the linear structure 20 from the state quantity U(t) obtained by simulation. w(t) is the observation error. The observation error w(t) can be treated by assuming that it follows an arbitrary probability distribution.

[0021] The observation matrix H is expressed by the following equation.

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[0022] When calculating the deflection angle θ of the linear structure 20, the observation matrix H is a (N+1)×9(N+1) matrix. In this embodiment, an example is shown in which the observation data is deflection angle data y and the simulation predicted value u extracted from the state quantity U is a displacement in the rotational direction, but this can be changed as appropriate depending on the combination of the observation data and the simulation predicted value.

[0023] The sequential data assimilation method uses a fusion particle filter, which creates multiple copies of particles according to their likelihood with the observed data, and updates the ensemble of particles by taking the weighted sum of the copies. The absolute likelihood of each particle is the sum of the observed data likelihoods for each element, and Observation data The likelihood was derived as a probability density function of a normal distribution, which was assumed to be defined by the average value of the rotational displacement and the standard deviation of the observation error.

[0024] The formulas for calculating the absolute likelihood and the relative likelihood are (4) and (5), respectively.

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[0025] Here, λ (i) (t) and γ(i) (t) are the absolute likelihood and relative likelihood of the i-th particle, respectively, and P n (i) (t) is the likelihood of the nth element in the ith particle, u n (i) (t|t-Δt) is the rotational displacement of the nth element in the ith particle, y n (t) is the deflection angle of the observed data of the corresponding part, W n (t) represents the observation error of the corresponding part.

[0026] 5 shows an example of a processing flow of the information processing unit 11. The processing flow of the information processing unit 11 includes steps S1 to S4. The information processing unit 11 executes step S1, and upon acquiring observation data, executes steps S2 to S4. In steps S2 to S4, the information processing unit 11 executes behavior estimation using a sequential data assimilation method.

[0027] Step S1: Uncertain parameters in a simulation model are expressed by a plurality of discrete values, and the behavior of the linear structure 20 is predicted using each of the discrete values. In this manner, a plurality of simulation predicted values ​​are generated. In this disclosure, the simulation predicted values ​​are referred to as particles. Step S2: When the observation data is acquired, the likelihood of each particle is calculated using the acquired observation data. At this time, the observation error may be taken into consideration as shown in formula (4). Step S3: At least one of the plurality of discrete values ​​is updated based on the likelihood, and likelihood-weighted resampling of particles is performed. Step S4: Time integration of each particle is performed using the simulation model, and system noise may be taken into account at this time. Each step is described in detail below.

[0028] Step S1: In considering a dynamic simulation of the linear structure 20, the expected range of an uncertain parameter (e.g., deflection angle θ) is expressed as discrete values ​​(θ1, θ2, ..., θ N), and a simulation predicted value is obtained for each case (called a particle). Discrete values ​​within the expected range are input, for example, from the input unit 14. The simulation is performed, for example, on a system with a length of 40 m, a diameter of 0.5 m, and a density of 1000 kg / m 3 Elastic rubber (Young's modulus: 5.0×10 5 A linear structure made of θ1, θ2, …, θ2 is suspended straight in still water, and the upper end is vibrated horizontally with a simple harmonic motion of 2 m in amplitude and 1.5 s in period for 10 seconds. N ) is applied. This allows the state quantity U(t) to be calculated using each parameter, and the horizontal displacement for each length L can be calculated.

[0029] When the optical fiber sensor 13 detects the strains ε1 and ε2 and the information processing unit 11 calculates the deflection angle θ, observation data for each length L is obtained, and steps S2 to S4 are sequentially repeated.

[0030] Step S2: The information processing unit 11 compares the obtained observation data with the expected observation error and each simulation prediction value to calculate the likelihood of each particle. For example, the absolute likelihood and relative likelihood for each length L are calculated using equations (3) and (4).

[0031] Step S3: Using the relative likelihoods obtained in step S2 as weights, resample the particles. For example, if the relative likelihoods of particles k', k'+1, and k'+2 are high and the relative likelihoods of other particles are low, increase the discrete values ​​of the parameter range used by particles k', k'+1, and k'+2, decrease the discrete values ​​of the parameter range other than particles k', k'+1, and k'+2, and resample the new parameter discrete values ​​(θ1, θ2, ..., θ N ) is generated. Then, a simulation prediction value is obtained using each parameter. This allows calculation of particles using parameters with high relative likelihood.

[0032] Step S4: Time integration is performed on the resampled particles using dynamic simulation. This allows the simulation predicted value at the time when the next observation data is acquired to be obtained for each element length L. The dynamic simulation is performed, for example, using the model used in step S1. Then, the process returns to step S2.

[0033] After steps S2 to S4 are repeated a predetermined number of times, a weighted average of a plurality of particles is taken for each element length L. Here, the number of times steps S2 to S4 are repeated may be a fixed number, or a configuration may be adopted in which the weighted average of a plurality of particles is taken when the relative likelihood falls below a certain value. In addition, the number of particles for which the weighted average is taken may be any number with a high relative likelihood.

[0034] As described above, in this embodiment, since the observation data by the optical fiber sensor 13 is sequentially taken in in step S2, the information processing unit 11 can estimate the behavior with high accuracy. Furthermore, in this embodiment, the overall distortion of the vertically long linear structure 20 containing a large amount of information is measured, and the likelihood taking into account the entire linear structure 20 is calculated using equation (4), so that the effect of improving the prediction accuracy of the linear structure 20 is obtained.

[0035] In this embodiment, an example is shown in which the uncertain parameter is the deflection angle θ, but the uncertain parameter can be any parameter used in a simulator that predicts the behavior of the underwater linear structure 20. For example, parameters used in a simulator that estimates the behavior of the underwater linear structure 20 include the tension T of the linear structure 20, the speed of the ship 100, the elasticity E of the linear structure 20, the cross-sectional area A of the linear structure 20, the velocity V of the linear structure 20 relative to the fluid around it, the mass m per unit length of the linear structure 20, the fluid density ρ around the linear structure 20, and the like. w , the tangential resistance coefficient C of the linear structure 20 t , the resistance coefficient Cn in the normal direction to the linear structure 20, the added mass coefficient Cmf in fluid acceleration motion, the added mass coefficient Cmb in element acceleration motion, and the diameter d of the linear structure 20.

[0036] When there are two or more uncertain parameters, particles are generated for each combination of uncertain parameters in step S1, and discrete values ​​in the parameter range are made dense for the parameter combination with high likelihood in step S3. As a result, the present disclosure has an effect of improving the prediction accuracy of the linear structure 20 by using a parameter combination with high likelihood even when there are two or more uncertain parameters.

[0037] (Example 2) This embodiment relates to the results of a simulation of behavior estimation to which the sequential data assimilation method shown in the first embodiment is applied. Length 40m, diameter 0.5m, density 1000kg / m 3 Elastic rubber (Young's modulus: 5.0×10 5 The effectiveness of the behavior estimation was verified using a model in which a linear structure 20 made of 1.5 Pa was suspended straight in still water and its upper end was vibrated horizontally with a simple harmonic motion at an amplitude of 2 m and a period of approximately 1.5 s for 10 seconds.

[0038] The simulation was performed with a time resolution of 0.001 seconds, a length L per element of 1 m, and a fluid density of 997 kg / m 3 The coefficients of the tangential resistance coefficient Ct, the normal resistance coefficient Cn, and the added mass coefficient Cmb were set to 1.5, 0.03, and 1, respectively. The observation data was the deflection angle θ for every 1 m of length obtained from the strain distribution of the linear structure, and the sampling rate was set to 25 Hz.

[0039] The number of weighted averages in the fusion particle filter is 3, and the weight coefficient is

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[0040] Sequential data assimilation was started 2 seconds after the start of the simulation, and the unknown parameters to be estimated were the modal damping ratios. The damping ratios of the first and second modes were assumed to be equal.

[0041] Figure 6 shows the shape estimation results for a linear structure 10 seconds after a simulation was performed without sequential data assimilation and with the modal damping ratio having uncertainty in the prior distribution. The vertical axis represents the depth distance, and the horizontal axis represents the horizontal distance. Coordinates (0,0) indicate the position of the linear structure 20 fixed to the ship 100 shown in Figure 1. It can be seen from Figure 6 that there is a particularly large uncertainty (estimation error) in the area where the horizontal amplitude is maximum.

[0042] The time evolution of the estimation error when sequential data assimilation is applied is shown in Figure 7. As the sequential data assimilation is applied (after 2 seconds), the estimation error is significantly reduced, and it can be seen that it has almost converged to the true value after 8 seconds from the application.

[0043] (Other embodiment examples) In the above-mentioned embodiment, the case where two optical fibers 21, 22 with the core interval d are used has been described as an example, but instead of the optical fibers 21, 22, a multi-core optical fiber 23 in which multiple cores 231, 232 are arranged at an interval d in the clad of one optical fiber as shown in Fig. 8 may be used. In addition, in Fig. 8, the multi-core optical fiber 23 with two cores is shown as an example, but the number of cores may be two or more, and any arrangement of the cores may be used. For example, a four-core fiber having one core at the center and three cores around it may be used.

[0044] (Effects of the present disclosure) This disclosure sequentially captures observation data from distributed sensors, enabling highly accurate real-time behavior estimation. Furthermore, when estimating the behavior of a vertically long linear structure that contains a large amount of information, this disclosure can improve the accuracy of behavior estimation by measuring the overall distortion compared to single-point measurement of the position coordinates of one point along the structure. [Industrial Applicability]

[0045] The present disclosure can be applied to the information and communications industry. [Explanation of symbols]

[0046] 10: Equipment 11: Information processing section 12: Storage part 13: Optical fiber sensor 14: Input section 20: Linear structure 21, 22: Optical fiber 23: Multi-core optical fiber 231, 232: Core 100: Ship

Claims

1. expressing parameters of the linear structure for each predetermined length as a plurality of discrete values, and predicting behavior of the linear structure using each of the discrete values; Obtaining the behavior of the linear structure detected using an optical fiber; Calculating a likelihood between the predicted behavior of the linear structure and the acquired behavior of the linear structure; updating at least one of the plurality of discrete values ​​based on the likelihood; Calculating a behavior of the linear structure using the updated discrete values. In the apparatus, the likelihood is calculated based on the sum of an average value of the rotational direction displacement of the linear structure derived for each of the predetermined lengths and a probability density function defined by a standard deviation of an observation error of the behavior of the linear structure detected using the optical fiber; Device.

2. an optical fiber sensor that detects a strain in the optical fiber, the optical fiber being disposed along the linear structure; using the strain detected by the optical fiber sensor to calculate a deflection angle per unit length of the linear structure as a parameter for each of the predetermined lengths of the linear structure, thereby acquiring a behavior of the linear structure; 2. The apparatus of claim 1.

3. The optical fiber sensor detects distortions of a plurality of optical fibers arranged along the linear structural object; Calculating a deflection angle per unit length of the linear structure using a difference in strain per unit length of the plurality of optical fibers.

3. The apparatus of claim 2.

4. the predicted behavior of the linear structure is a displacement in a rotational direction per unit length of the linear structure, calculating the likelihood using the predicted displacement in a rotational direction per unit length of the linear structure and the calculated deflection angle per unit length of the linear structure; 4. Apparatus according to claim 2 or 3.

5. predicting an updated behavior of the linear structure using the updated discrete values; weighting the updated predicted behavior of the linear structure according to the likelihood; Calculating the behavior of the linear structure by averaging the weighted behavior of the linear structure.

5. Apparatus according to any one of claims 1 to 4.

6. expressing parameters of the linear structure for each predetermined length as a plurality of discrete values, and predicting behavior of the linear structure using each of the discrete values; Obtaining the behavior of the linear structure detected using an optical fiber; Calculating a likelihood between the predicted behavior of the linear structure and the acquired behavior of the linear structure; updating at least one of the plurality of discrete values ​​based on the likelihood; calculating a behavior of the linear structure using the updated discrete values; In the method, the likelihood is calculated based on the sum of an average value of the rotational direction displacement of the linear structure derived for each of the predetermined lengths and a probability density function defined by a standard deviation of an observation error of the behavior of the linear structure detected using the optical fiber; method.

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