The present disclosure relates to an apparatus and methods for estimating the behavior of a linear structure in water, such as a submarine cable, by means of reflectometry technology using an optical fiber.
A method for detecting the behavior of a linear structure in water, such as a submarine cable, by using an optical fiber sensor has been proposed. An optical fiber sensor is technology for measuring and analyzing a reflection spectrum of an optical fiber by using OFDR (Optical Frequency Domain Reflectometry) to derive a three-dimensional shape of a measured target. Fiber optic sensors are capable of dynamic measurements over long distances. However, in the monitoring of a linear structure in water, there is the problem of an accumulation of errors due to integral calculations along the optical fiber.
In addition, as a method suitable for estimating a phenomenon in real time, there exists the example of behavior estimation using sequential data assimilation in which data assimilation is performed for each obtainment of time observation data (see, for example, Non Patent Literature 1). However, this method employs, as observation data, discrete position information of a linear structure acquired by a global positioning system (GPS) or the like. In order to acquire the position information, it is necessary to receive radio waves in water. Therefore, as the depth in water increases, acquiring the position information becomes problematic and obtaining continuous data in the length direction becomes difficult.
Non Patent Literature 1: J. V. 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.
An object of the present disclosure is to enable the behavior of a linear structure in water to be estimated.
An apparatus and a method according to the present disclosure include:
The present disclosure enables the behavior of a linear structure in water to be estimated.
Hereinafter, 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 following embodiments. These examples are merely examples, and the present disclosure can be carried out in a variety of forms obtained through modifications and improvements based on the knowledge of those skilled in the art. Note that components having the same reference signs in the present specification and the drawings indicate the same components.
Behavior of the linear structure 20 is, for example, three-dimensional coordinates of the linear structure 20. The three-dimensional coordinates of the linear structure can be calculated using the displacement in the rotation direction of the linear structure 20 with respect to the position of at least one point of the linear structure 20 from which the position information can be acquired. Therefore, in the present embodiment, an example in which the behavior of the linear structure 20 is displacement in the rotation direction for each length L of the linear structure 20 is described.
The optical fiber sensor 13 detects values of strain ε1 and ε2 in the two optical fibers 21 and 22. An optical fiber sensor using a BOTDR (Brillouin Optical Time Domain Reflectometer) is an example of means for detecting values of strain in the optical fibers 21 and 22, for example. In the following description, a case where the optical fiber sensor 13 is a BOTDR is assumed.
The information processor 11 calculates behavior of the linear structure 20 by using the strain detected by the optical fiber sensor 13. The displacement of the linear structure 20 in the rotation direction can be obtained using the length L of the linear structure 20 and a deflection angle θ[rad] with respect to the length L of the linear structure 20. Therefore, the information processor 11 calculates the deflection angle θ[rad] with respect to each length L of the linear structure 20 by using the values of the strain 21 and 22 of the linear structure 20. Hereinafter, an example in which the information processor 11 calculates the deflection angle θ[rad] with respect to each length L of the linear structure 20 as the behavior of the linear structure 20 is described.
Furthermore, the information processor 11 forecasts behavior of the linear structure 20 by using a simulator. For example, the information processor 11 uses freely selected parameters to simulate the behavior of the linear structure 20 and calculates the state quantity U(t). The information processor 11 uses a state quantity U(t) to calculate displacement in the rotation direction with respect to each length L of the linear structure 20.
In addition to the values of the strain ε1 and ε2 detected by the optical fiber sensor 13, the storage unit 12 stores any data used for the processing by the information processor 11 and stores the processing result of the information processor 11. The data used for the processing by the information processor 11 includes a simulation program for forcasting the behavior of the linear structure 20 and parameters used by the simulation program. The apparatus 10 according to the present embodiment can also be realized by a computer and a program, and the program can be recorded on a recording medium or provided over a network. Details will be described hereinbelow.
The two optical fibers 21 and 22 are placed along the linear structure 20 in water, and as illustrated in
When the length L is the unit length for forecasting the behavior of the linear structure 20, the deflection angle θ in Formula (1) corresponds to the displacement in the rotation direction, which is obtained as a simulation forecasted value. For example, as illustrated in
Given that the observation data of a strain distribution detected by the optical fiber sensor 13 is converted into deflection angle data y(t) for each length L, Formula (2) is derived.
[Formula 2]
y(t)=HU(t)+w(t) (2)
Here, H is an observation matrix for extracting the displacement of the linear structure 20 in the rotation direction from the state quantity U(t) obtained by simulation. w(t) is an observation error. The observation error w(t) can be handled by assuming that same follows any probability distribution.
The observation matrix H is represented by the following formula.
When the deflection angle θ of the linear structure 20 is calculated, the observation matrix H is a matrix (N+1)×9(N+1). In the present embodiment, an example is illustrated in which the observation data is the deflection angle data y, and a simulation forecasted value u extracted from the state quantity U is the displacement in the rotation direction, but changes can be made as appropriate, according to the combination of the observation data and the simulation forecasted values.
In the sequential data assimilation method, a merging particle filter is used, and a plurality of particles are replicated according to the likelihood together with observation data, and the ensemble, which is a set of particles, is updated by taking the weighted sum. The absolute likelihood of each particle is the infinite product of the observation data likelihood for each element, and for the relative likelihood of each element, a normal distribution, defined by the average value of the displacement in the rotation direction and the standard deviation of the observation error, is assumed and derived as a probability density function of the normal distribution.
Formulae (4) and (5) are used to calculate the absolute likelihood and the relative likelihood, respectively.
Here, λ(i)(t) and γ(i)(t) represent the absolute likelihood and the relative likelihood of the i-th particle, respectively; Pn(i)(t) represents the likelihood of the n-th element in the i-th particle, un(i)(t|t−Δt) represents the displacement in the rotation direction of the n-th element in the i-th particle; yn(t) represents the deflection angle of the observation data of the corresponding portion; and Wn(t) represents the observation error of the corresponding portion.
Hereinafter, each step will be described in detail.
Once the optical fiber sensor 13 detects the values of the strain ε1 and ε2 and the information processor 11 calculates the deflection angle θ to obtain the observation data for each length L, steps S2 to S4 are sequentially repeated.
After steps S2 to S4 are repeated a predetermined number of times, a weighted average of the plurality of particles is taken for each length L of the element. Here, the number of repeats of steps S2 to S4 may be a certain number, but the setup may be such that a weighted average of a plurality of particles is taken on the occasion of the relative likelihood being below a certain value. In addition, as the number of particles whose the weighted average is taken, any number having a high relative likelihood can be adopted.
As described hereinabove, in the present embodiment, because the observation data by the optical fiber sensor 13 is sequentially fetched in step S2, the information processor 11 is capable of performing highly accurate behavior estimation. Furthermore, in the present embodiment, because the strain of the entire vertically long linear structure 20, having a large amount of information, is measured, and the likelihood, taking into account the entire linear structure 20, is calculated using Formula (4), it is possible to attain the advantageous effect of enabling an enhanced forecast accuracy for the linear structure 20.
In the present embodiment, an example in which the uncertain parameter is the deflection angle θ is illustrated, but the uncertain parameter may be any parameter used in a simulator that forecasts the behavior of the linear structure 20 in water. For example, the parameters used in the simulator for estimating behavior of the linear structure 20 in water include the tension T of the linear structure 20, the velocity 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 with respect to the fluid around the linear structure 20, the mass m per unit length of the linear structure 20, the fluid density ρw around the linear structure 20, the resistance coefficient Ct in the tangential direction of the linear structure 20, the resistance coefficient Cn in the normal direction with respect to the linear structure the additional mass coefficient Cmf in the fluid acceleration motion, the additional mass coefficient Cmb in the element acceleration motion, the diameter d of the linear structure 20, and the like.
Note that, in a case where there are two or more uncertain parameters, a particle is generated for each combination of uncertain parameters in step S1, and discrete values of a parameter range are densified for a combination of parameters having a high likelihood in step S3. Accordingly, the present disclosure affords the advantageous effect of enabling an enhanced forecast accuracy for the linear structure 20 by using a combination of high likelihood parameters, even in a case where there are two or more uncertain parameters.
The present embodiment relates to a simulation result of behavior estimation to which the sequential data assimilation method described in the first embodiment is applied.
The advantageous effect of the behavior estimation was verified using a model in which a linear structure 20 made of elastic rubber (Young's modulus: 5.0×103 Pa), having a length of 40 m, a diameter of 0.5 m, and a density of 1000 kg/m3, is hung straight in still water, and the upper end of the linear structure was subjected to single vibration in the horizontal direction with an amplitude of 2 m and a period of about 1.5 s for 10 seconds.
For the simulation, the time division was 0.001 second, the length L per element was 1 m, the fluid density was 997 kg/m3, and the coefficients of the tangential resistance coefficient Ct, the normal resistance coefficient Cn, and the additional mass coefficient Cmb were 1.5, 0.03, and 1, respectively. The observation data was the deflection angle θ with respect to each length of 1 m obtained from the strain distribution of the linear structure, and the sampling rate was 25 Hz.
The number of weighted averages taken in the merging particle filter was 3, and the weighting factor was set as
[Formula 6]
α1=19/20
α2=(1+√{square root over (77)})/40)
α3=(1−√{square root over (77)})/40) (6)
Here, α1 is a weight of a particle having the highest relative likelihood, α2 is a weight of a particle having the second highest relative likelihood, and α3 is a weight of a particle having the third highest relative likelihood.
The start of the sequential data assimilation was after 2 seconds from the start of the simulation, and the unknown parameters to be estimated were mode attenuation ratios. It is assumed that the attenuation ratios of the primary mode and the secondary mode are equal.
Note that although, in the above-described embodiment, a state where the cores of the two optical fibers 21 and 22 have the interval d therebetween, was described as an example, instead of the optical fibers 21 and 22, one multicore optical fiber 23 in which a plurality of cores 231 and 232 are arranged to have the interval d in the cladding of the optical fiber, as illustrated in
Because, according to the present disclosure, observation data is sequentially fetched using a distribution-type sensor, highly accurate real-time behavior estimation can be performed. Furthermore, according to the present disclosure, when estimating behavior of a vertically long linear structure having a large amount of information, by measuring the entire strain, the accuracy of the behavior estimation can be enhanced in comparison with a case where the position coordinates of one intermediate point are measured using single point measurement.
The present disclosure can be applied to the information communication industry.
Number | Date | Country | Kind |
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2020-185198 | Nov 2020 | JP | national |
Filing Document | Filing Date | Country | Kind |
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PCT/JP2021/038481 | 10/18/2021 | WO |