KR20120085415A - Method for measuring temperature using optical fiber - Google Patents

Abstract

PURPOSE: A temperature measuring method using an optical fiber is provided to have small errors because an interpolating polynomial is used for calculation, thereby accurately measuring temperature distribution regardless of a distance even a long distance. CONSTITUTION: A temperature measuring method using an optical fiber is as follows. An nth interpolating polynomial is obtained by using predetermined equation with n+1 numbers of data which are different each other. A temperature of an arbitrary position is calculated by using the obtained nth interpolating polynomial. The temperature of the arbitrary position is accurately measured by using the interpolating polynomial according to Lagrange Interpolation. The temperature with respect to a long distance and an extended section can be measured.

Description

Temperature measurement method using optical fiber {METHOD FOR MEASURING TEMPERATURE USING OPTICAL FIBER}

The present invention relates to a temperature measuring method using an optical fiber, and more particularly, by measuring (calculating) a temperature at an arbitrary point using an interpolation polynomial according to the LaGrange interpolation method, an accurate temperature distribution The present invention relates to a temperature measuring method using an optical fiber that can measure and measure temperature in a long distance as well as an extended section.

In measuring the temperature distribution of an optical composite cable of power transmission and distribution, optical fiber is used as a temperature sensor. In this case, an optical time domain reflectometer (OTDR) is generally applied to a distributed temperature system (DTS) to measure temperature according to a distance (position). Specifically, when pulsed light is incident on one end of the optical fiber, λs strokes light and Raman scattered light of λas anti-strokes light are generated. The ratio of these two Raman scattered light is a function of pure temperature, which can lead to the relationship between Raman scattered light intensity and temperature. The distance (position) of scattered light is calculated by measuring the speed of light in the optical fiber and the elapsed time of returning light using the OTDR principle. That is, the distance (position) of the scattered light is calculated by calculating the elapsed time of the returning light, and the temperature according to the distance (position) may be measured by using the relationship between the scattered light intensity and the temperature of the distance (position).

As above, the linear temperature distribution around the optical fiber can be measured using the DTS and OTDR principles. The temperature measurement using the principle of the DTS and OTDR is mainly used for measuring the temperature distribution of the cable, Korean Patent Publication No. 1993-0001186, Korean Patent Publication No. 2003-0095523 and Korean Patent Registration No. 10-0935529 Is presented. Optical fiber temperature measurement using Raman scattered light is useful for measuring the longitudinal temperature distribution of power (transmission and distribution) cable, which is used for transmission / distribution capacity control, and it is possible to find the place of partial high heat generated by deterioration of cable. It is useful for detecting.

Multi-mode and single-mode optical fibers are used as sensors to measure the temperature of fiber-optic cable, and single mode is mainly used for long distance measurement. In particular, in the case of the distribution cable, unlike the transmission cable, it is installed inside the city center, and passes through or bypasses existing facilities, and passes through various paths, and thus, a complicated structure and many temperature measurement sections are generated. In general, the DTS can measure temperature within a distance of about 12 km, and additional DTSs must be installed to measure more distance.

However, the conventional temperature measurement method, that is, the method using the OTDR principle as described above has a large error because it is calculated by dividing the time uniformly over the entire interval. That is, the temperature may have a non-linear value with no regularity depending on the distance (position), but the conventional method using the OTDR principle merely calculates (estimates) the temperature by expressing it as a linear graph between the measurement intervals. There is a big problem. In addition, it takes a long calculation time for the fine section, there is a problem that the storage space of the DTS is insufficient because a lot of data is stored.

In addition, the conventional method for measuring temperature using the OTDR principle has difficulty in calculating (estimating) a temperature for a specific location or a long distance. In other words, the temperature measurement method using the OTDR principle is represented by a linear graph, it is possible to measure (estimate) the temperature at any point (position) existing between the measurement intervals, but it is not possible to install an extension section or an optical fiber It is difficult to measure (estimate) temperature over difficult periods and over long distances.

Thus, the present invention by using the interpolation polynomial according to the LaGrange interpolation method, it is possible to measure the temperature distribution precisely because the error is small, and the temperature can be measured without restriction on a specific distance (position), such as long distance as well as an extended section, It is an object of the present invention to provide a temperature measuring method using an optical fiber.

The present invention to achieve the above object,

N-th interpolation polynomials of different n + 1 (n is an integer greater than or equal to 1) measurement data (temperature according to position) are obtained by using Equation 1 below, and the n-th interpolation polynomials are obtained at any position. It provides a temperature measuring method using an optical fiber, including the step of calculating the temperature for.

[Equation 1]

In Equation 1 above,

          x = any location where temperature is to be measured,

P _n (x) = temperature at any position (x),

y _i = the given function value (temperature) at n + 1 positions,

L _i (x) is represented by Equation 2 below.

&Quot; (2) "

The temperature measuring method according to the present invention can be usefully used, for example, in measuring the temperature distribution of a power transmission or distribution cable.

According to the present invention, in measuring the temperature using the optical fiber, it is calculated (measured) through the interpolation polynomial of the above equation, so that the error is small and accurate temperature distribution can be measured. In addition, it is possible to measure the temperature without restriction on the distance (position), such as long distance as well as the extension section.

1 is a graph for comparing and comparing the prior art and the present invention, and is a linear graph and a polynomial graph for explaining a temperature measuring method for a detailed position in a measurement section.
2 is a graph for comparing the present invention with the prior art, and is a linear graph and a polynomial graph for explaining a method of measuring a temperature for an extended section.
3 is a graph illustrating a method of measuring a temperature for a minute section existing within a measurement section according to the present invention.
4 is a graph for explaining a method of measuring the temperature of the extended section out of the measurement section in accordance with the present invention.

Hereinafter, the present invention will be described in detail.

The temperature measuring method using the optical fiber according to the present invention (hereinafter, abbreviated as "temperature measuring method") uses an interpolation polynomial according to the LaGrange interpolation method. The Lagrange interpolation polynomial applied to the present invention is a kind of interpolation method using polynomials, and has a merit of simpler calculation and less error than undecided coefficient method or Newton interpolation polynomial, as well as the method using the conventional OTDR principle. . Lagrangian interpolation polynomials are used to estimate data within a given interval or to obtain predictions based on given data.

Lagrangian interpolation uses (k-1) th order polynomials generated from k given points (values you already know), and the final equation is (k +). a-1) becomes a polynomial At this time, the (k-1) th polynomial and the (k-a + 1) th polynomial are different from each other, but the shape of the graph is similar.

The present invention obtains the output graph (xy coordinate, x: position, y: temperature) of the temperature according to the position (distance) using the Lagrangian interpolation method, that is, the Lagrange interpolation polynomial, and any optical fiber to be measured through The temperature at the location can be calculated (measured). At this time, in order to use the Lagrangian interpolation polynomial, as the measured data (given value), n + 1 temperature values according to the position (n is an integer of 1 or more), that is, at least two or more measurement data (temperature according to the position) ) Exists. These n + 1 measurement data may be actual values, or may be a value calculated according to a conventional method. An nth-order interpolation polynomial is obtained using the Lagrange interpolation polynomial based on the n + 1 measurement data. And the temperature for any position (distance) can be calculated using the obtained n-th interpolation polynomial. In other words, it is possible to calculate the minute point or the data outside the section within a given section. At this time, the temperature according to each position is represented by the polynomial graph by the interpolation polynomial.

Specifically, the method for measuring temperature according to the present invention obtains an n-th interpolation polynomial using Equation 1 through data of n + 1 (n is an integer greater than or equal to 1) data (temperature according to position), and the obtained calculating a temperature for any location using an n-th interpolation polynomial.

[Equation 1]

In this case, L _i (x) in Equation 1 is a Lagrangian coefficient polynomial, which is represented by Equation 2 below.

&Quot; (2) "

In Equations 1 and 2, x is an arbitrary position where the temperature is to be calculated (measured), that is, an arbitrary point of the optical fiber whose ambient temperature is to be measured, and P _n (x) is the arbitrary position (x). The temperature at, i.e. the temperature value to be calculated (measured). And y _i is the temperature as a given function value f (x _i ) at each n + 1 positions x _i , and i and j are integers greater than or equal to zero. I and j = n + 1.

In this case, Equation 1 may be represented by a developed equation represented by Equation 1-1 below, and Equation 2 may be expressed by a developed equation represented by Equation 2-1 below.

[Equation 1-1]

[Equation 2-1]

More specifically, given data (position, temperature), n + 1 different data, that is, (x ₀ , y ₀ ), (x ₁ , y ₁ ), ... (x _n , y _n ) Given the value of, substituting the given values into Equations 1 and 2 yields an n-th interpolation polynomial. Then, by substituting an arbitrary position value x for which temperature is to be known into the obtained n th interpolation polynomial, the temperature at the position x can be calculated. At this time, the nth interpolation polynomial may be one or more than two. When the n-th interpolation polynomial is found to be two or more plural numbers, one final n-th interpolation polynomial is obtained by combining them, and the temperature is calculated by substituting arbitrary position values (x) into the final n-th interpolation polynomial.

In addition, the n + 1 data (position, temperature) are already obtained values, which may be actual measured values measured using a temperature / distance meter or the like, or may be values calculated using a conventional OTDR principle. . According to an exemplary embodiment of the present invention, the n + 1 data (position, temperature) may use a value calculated by a method using a conventional OTDR principle, which specifically determines the time difference of the returning light. The distance (position) in which scattered light is generated can be calculated, and the calculated value (temperature according to distance) can be used by using the relationship between scattered light intensity and temperature of the distance (position).

According to the present invention, it is possible to calculate a detailed temperature for a minute section, and to accurately measure the temperature distribution, compared to a method using only the conventional OTDR principle. And the calculation is simple, saving time. In addition, temperature measurement can be performed not only for long distances but also for extended sections. This will be described in more detail with reference to the accompanying drawings.

First, referring to FIGS. 1 and 2, a method using a conventional OTDR principle and a method using a Lagrange interpolation polynomial of the present invention will be described. 3 and 4 illustrate a specific temperature calculation method in the measurement section and the extension section using the Lagrange interpolation polynomial (Equations 1 and 2) according to the present invention.

1 is a graph illustrating a comparison between a method using a conventional OTDR principle and a method using a Lagrange interpolation polynomial of the present invention, and is a temperature graph in a measurement section (detailed position).

In Figure 1, a and b are two different position values measured at regular time intervals, and R is the difference between two different positions measured at regular time intervals (distance difference = b-a). F (a) and F (b) are two different temperature values for two different positions measured, and FO-1 is a graph generated by applying a conventional OTDR method (hereinafter referred to as a 'linear graph'). , FL-1 is a graph generated using the Lagrangian interpolation polynomial according to the present invention (hereinafter referred to as 'polynomial graph').

The conventional OTDR method generates a continuous linear graph FO-1 by utilizing coordinate values that are sequentially read out of temperature values for each location. However, the present invention is applied to detail the conventional OTDR method of estimating distance by sampling by dividing by time difference. A disadvantage of the linear graph (FO-1) calculated by the OTDR method is that there is no correlation between the data before and after because the data is independent without continuity between the data. For this reason, there is no correlation between the data, so it is difficult to express the section other than the section represented by the data. In order to overcome this problem, the present invention applies a Lagrangian interpolation polynomial to generate a graph using an arbitrary representative point in a section to estimate a temperature distribution.

As shown in Fig. 1, the linear graph FO-1 has the same value as the interpolated polynomial graph FL-1 in the value of the temperature according to each position a and b. That is, in estimating the positions of two points, they may be the same as the linear graph FO-1 and the polynomial graph FL-1. However, in the conventional method of estimating the linear graph FO-1, when the positions of the two points are connected to each other, an error occurs because the temperature value at an arbitrary point inside the two distance differences R is ignored. The linear graph FO-1 can only be estimated as a value proportional to the distance. Accordingly, the linear graph FO-1 shows a large error for any position existing inside the two distance differences R. As shown in FIG. Since the temperature value measured according to the distance is a nonlinear value without regularity, an error occurs when the graph is represented linearly, and it is difficult to accurately estimate the position of the distance difference (R).

However, since the polynomial graph (FL-1) applied to the present invention, not the linear graph (FO-1), is estimated as a graph including all the points in consideration of an error for any point, the distance difference (R) is Even if it occurs, the error for the short section is negligibly small, so the temperature value can be estimated at any point. That is, if a Lagrangian interpolation polynomial is derived for a point belonging to a section, an accurate temperature value can be estimated at any point within the section. In this case, it is preferable to calculate and apply a Lagrangian interpolation polynomial of 2 to 6 orders in order to reduce the error of the short interval. In other words, it is preferable to obtain and apply 3 to 7 measurement data (given values) to the second to sixth order interpolation polynomials.

In addition, although the linear graph FO-1 according to the conventional OTDR has difficulty in estimating the temperature value for a specific position (extension section, etc.), the polynomial graph FL-1 is not limited to the specific position, Estimation is possible. This will be described with reference to FIG. 2.

FIG. 2 is a graph for comparing a conventional method using the OTDR principle and a method using the Lagrange interpolation polynomial of the present invention, and a graph for measuring a temperature of a position existing on an extension distance line.

In FIG. 2, a 'and b' are two different position values measured at regular time intervals, which are the last position values of the measurement interval (where a ≠ a 'and b ≠ b' in FIG. 1), and R ' Is the final distance difference between the measurement intervals of the two different positions measured at regular time intervals, and c 'is an arbitrary position on the extended section line outside the measurement interval (measured position). And F (a ') and F (b') are two different temperature values for two different positions measured, except that F (a) ≠ F (a ') and F (b) ≠ F ( b '), and F (c') is the measured temperature value at an arbitrary point c 'on the extension section line. In addition, FO-2 is a graph generated by applying the conventional OTDR method (hereinafter, a linear graph) including an extension section, FL-2 is a graph generated using the Lagrange interpolation polynomial according to the present invention It is a graph including an extension section (hereinafter, polynomial graph).

The graph of FIG. 2 shows the measurement principle at R ″ including an extension section outside the measurement section.

Referring to FIG. 2, in the conventional OTDR method, since the measurement temperature divided by a predetermined time interval and calculated by 1: 1 for each position is expressed as a linear graph (FO-2), the data constituting the graph are independent of each other. to be. Therefore, even if the position value c 'on the extended section line is given, an appropriate value of F (c') cannot be obtained in the linear graph, but only an estimated value based on the linear graph.

However, since the data constituting the polynomial graph (FL-2) using the Lagrange interpolation polynomial according to the present invention is dependent on each position and the measured temperature, even if there is any position value c 'on the extension section line, It can be expressed by inferring the measured temperature value of F (c '). In addition, when divided into small intervals, when using the Lagrangian interpolation polynomial according to the present invention, there is no section in which the temperature is rapidly changed in the adjacent position, the temperature value determined at the position of c 'is affected by the previous measurement data. Therefore, in the case of using the interpolation polynomial, it is possible to calculate the previous value by estimating the previous value even if the actual measurement is not performed on the extended section line outside the measurement section.

With reference to the above implementation, a specific method for calculating the temperature value in any section (detailed section) that is not represented in a given section (measured section) and the temperature value in the extended section is shown in FIGS. 3 and 4. Referring to the following.

First, a method of measuring (estimating) a temperature value in an arbitrary section (detailed section) that is not represented within a given section (measured section) will be described with reference to FIG. 3.

In Figure 3,

TR: the whole measurement section

Px: Arbitrary distance data within the entire measurement interval

F (Px): Temperature data according to the distance data within the entire measurement section

P1, P2, P3: any continuous distance data within the entire measurement interval

DN1: Distance data group including distance data of P1, P2, P3

DN2: Distance data group including distance data of P2, P3, P4

F (P1), F (P2), F (P3), F (P4): Temperature data derived from the distance data of P1, P2, P3, P4

F (DN1): Interpolation polynomial formed by coordinates (P1, F (P1)), (P2, F (P2)), (P3, F (P3))

F (DN2): Interpolation polynomial formed by coordinates (P2, F (P2)), (P3, F (P3)), (P4, F (P4)).

First, the data of the distance and the temperature for the entire measurement section TR can be obtained, for example, by the OTDR method or by the actual measurement through a measuring instrument. Hereinafter, the data obtained by the OTDR method will be described as an example.

By the OTDR method, temperature data calculated 1: 1 is calculated according to the distance data. When a user (measurer) wants to obtain a desired temperature at an arbitrary distance within the entire measurement section TR, it can be calculated as follows.

At this time, let arbitrary distance data desired be Px. To calculate the temperature value for the distance Px, find the position range that Px belongs to. When searching for the location range, distance data having a predetermined interval measured by OTDR may be used as described above. As shown in FIG. 3, assuming that the position of Px exists between P2 and P3, the Lagrangian third order polynomial basic equation (E1) is obtained by using the value of DN1 formed by the distance data group of P1, P2, and P3. ), We can obtain a polynomial (F (DN1)) including F (Px).

P (x) = y ₀ L ₀ (x) + y ₁ L ₁ (x) + y ₂ L ₂ (x) ....... (E1)

In addition, Px can obtain a polynomial (F (DN2)) including F (Px) in the Lagrange third-order polynomial basic formula (E1) using the value of DN2 formed by the distance data group of P2, P3, and P4.

When the two polynomials, ie, F (DN1) and F (DN2) polynomials, are obtained, a final polynomial called F (Px) can be obtained, and temperature data for a distance Px can be obtained through the final polynomial. .

As described above, two third order polynomials are obtained through P1, P2, P3, and P4, and through this, temperature for any point Px in a detailed section can be obtained. Also, as another example, one polynomial can be obtained from given data for three points, and the temperature for any point in the detail interval can be obtained through this.

As a specific example, the measurement data (given value) is within (1, 2), (2, 4), (3, 3) within the measurement interval (position) 1 to 3 (starting point: 1, end point: 3). Assuming that the interpolated polynomial is obtained using the values given above,

First, by substituting the given values y ₀ = 2, y ₁ = 4, and y ₂ = 3 into Equation 1, the following quadratic interpolation polynomial is obtained.

And if you expand equation (2),

,

,

,

,

to be.

Next, substituting the values of L ₀ (x), L ₁ (x) and L ₂ (x) into the second-order interpolation polynomials is as follows.

At this time, for example, to know the temperature at the 1.5 position (point) as the position in the measurement interval 1 to 3, if x = 1.5 is substituted into the final quadratic polynomial obtained, P ₂ (x) The value is calculated as "3.375". That is, the temperature at the 1.5 position (point) becomes "3.375".

Next, a method of measuring (estimating) a temperature value in an extension section will be described with reference to FIG. 4.

In Figure 4,

TR: the whole measurement section

Px ': arbitrary distance data within the entire measurement interval

F (Px '): Temperature data according to the distance data in the entire measurement section

P1 ', P2', P3 ', P4': any continuous distance data within the entire measurement interval

DN1 ': distance data group including distance data of P2', P3 ', P4'

DN3: Distance data group including distance data of P2 ', P3', P4 ', Px'

F (P1 '), F (P2'), F (P3 '), F (P4'): Temperature data derived from the distance data of P1 ', P2', P3 ', P4'

F (DN1 '): Interpolation polynomial formed by coordinates (P2', F (P2 ')), (P3', F (P3 ')), (P4', F (P4 '))

F (DN3): Coordinates (P2 ', F (P2')), (P3 ', F (P3')), (P4 ', F (P4')), (Px ', F (Px')) Interpolation polynomials formed

S1: Area of the polynomial of F (DN1 ') in the interval P3' to Px '

S2: Area of the polynomial of F (DN3) in the interval P2 'to Px'

S3 is the area of the polynomial of F (DN3) in the interval P2 'to P3'.

First, as described above, data of the distance and the temperature for the entire measurement section TR may be obtained by, for example, the OTDR method or by actual measurement by a measuring instrument. The following describes a method of calculating the temperature in an extended section, taking the example of using data obtained by the OTDR method.

By the OTDR method, temperature data calculated 1: 1 is calculated according to the distance data. When a user wants to obtain a desired temperature at an arbitrary distance outside the entire measurement section TR, it can be calculated as follows.

At this time, desired arbitrary distance data is called Px '. The interpolation polynomial is obtained using the given coordinates to find the temperature value F (Px '), that is, the unknown value for the distance Px'. In calculating the temperature in the extension section, as described with reference to FIG. 3, the interpolation polynomial in the entire measurement section TR is obtained, and the arbitrary interpolation polynomial in the extension section is used to determine the arbitrary distance data Px 'in the extension section. Although it is possible to obtain a temperature for the temperature, it is possible to calculate a more accurate temperature by using the area as follows.

That is, to find F (Px '), which is a temperature value for the distance Px', an interpolation polynomial is obtained using the given coordinates, the area is obtained using the polynomial, and then the value of F (Px ') is used. Obtain

Referring specifically to FIG. 4, first, an interpolation polynomial F (DN1 ') including F (Px') is obtained for the data soldier DN1 'for P3', P4 ', and Px'. The area is calculated from P3 'to Px' using the obtained polynomial (F (DN1 ')). That is, the area from P3 'to Px' is obtained by integrating the obtained polynomial F (DN1 '). The area obtained at this time is called S1.

Next, an interpolation polynomial F (DN3) including F (Px ') is obtained for the data soldier DN3 from P2' to Px. The area from P2 'to Px' is obtained using the obtained polynomial (F (DN3)). The area obtained at this time is called S2.

In addition, the area from P2 'to P3' in the interpolation polynomial (F (DN3)) is called S3.

In this case, the obtained area is a relational expression of S2 = S3 + S1, and using the above equation, F (Px ') is derived. Thus, the temperature for any distance Px 'existing in the extension section can be obtained using the final F (Px') obtained through the three polynomials, i.e., the planes S1, S2 and S3.

As described above, the present invention obtains one or two or more n-order interpolation polynomials using Lagrangian interpolation polynomials (ie, Equations 1 and 2) based on n + 1 measurement data (given values). It is possible to measure (calculate) the temperature using the polynomial obtained above. According to the invention, as described above, the temperature for any point in the measurement interval, i.e. the temperature for any point existing between the given values, as well as the temperature for any point existing in the extension section outside the measurement interval. Can be measured. And the small error allows accurate temperature distribution measurement.

The present invention is usefully applied to the measurement of the temperature around the optical fiber is laid, preferably to the temperature measurement of the power transmission or distribution cable. And, by measuring the temperature of the transmission / distribution cable, it is possible to detect the location of the partial high heat generated by the capacity control of the transmission / distribution, deterioration of the cable.

Claims (2)

The nth interpolation polynomial is obtained from the following n + 1 (n is an integer greater than or equal to 1) data (temperature according to the position) using Equation 1 below, and the arbitrary position is obtained using the obtained nth interpolation polynomial. Temperature measurement method using an optical fiber comprising the step of calculating the temperature for:

[Equation 1]

In Equation 1 above,
x = any location where temperature is to be measured,
P _n (x) = temperature at any position (x),
y _i = the given function value (temperature) at n + 1 positions,
L _i (x) is represented by Equation 2 below.

&Quot; (2) "

The method of claim 1,
The temperature measuring method using the optical fiber is a temperature measuring method using the optical fiber, characterized in that the temperature measuring method of the transmission or distribution cable.

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