JP2014109088A - Correction quantity calculation system for curve correction, and computer program for correction quantity calculation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve reliability of a calculation result in calculation of a correction quantity for curve correction.SOLUTION: A correction quantity calculation system 1 includes an input part 2, a processing part 4, and an output part 4. The processing part 3 includes a design versine calculation part 31 which calculates a design versine of a curve having been corrected based upon a measurement versine, a curve length, and a transition curve length input to an input part 2, and a correction quantity calculation part 32 which calculates a correction quantity at each measurement point from the design versine and measurement versine. The design versine calculation part 31 calculates the design versine so that the design versine has the curve length and transition curve length, the sum in a measurement section is equal to the sum of the measurement versine, and the sum of moment is equal to the sum of moment of the measurement versine. The correction quantity calculation part 32 calculates the correction quantity by using inverse matrix from the design versine and measurement versine. Thus, the correction quantity which corrects the curve length and transition curve length of the design versine into input values can be obtained as a unique solution.

Description

  The present invention relates to a correction amount calculation system and a correction amount calculation computer program for calculating a correction amount for correcting a curve on a railway track.

  Since a railway track is deformed by repeatedly receiving a train load, it is necessary to repair the track by grasping the deformation of the track in maintenance of the railway. In the deformation of the orbit, there is an orbital displacement on a plane alignment called a passage displacement. In particular, since the track in the curved section receives a centrifugal force from the train, the displacement is likely to occur. The curve section has a circular curve and a relaxation curve. A circular curve is an arc. The relaxation curve is a curve of a transition section between a straight line and a circular curve. Curve correction is to prepare a correct curve by maintaining the trajectory of the curve section where the displacement has occurred.

  For the curve correction, the intersection method in the yarn tension type curve correction has been used for a long time (see Non-Patent Document 1). In the yarn tension type curve rectification, the curve is rectified on the basis of an arrow which is a distance from a string made of a thread stretched between two points to a point on the curve. The arrow at the center of the string is called Masaya. In the crossing method, which is an application of the circle distance method, the measurement of Masaya when a yarn is stretched between adjacent measurement points is performed at all the measurement points with 1/2 feed of the yarn length. According to the intersection method, the distance between both curves is calculated from the design arrow that is the correct arrow of the correct curve after correction, and the measurement arrow that is the correct arrow measured on the field curve, and the interval is corrected. The field curve is moved to match the correct curve as a quantity. The correction amount is also called a movement amount.

  However, it is not easy to obtain a correct curve or a design arrow after correction based on the measurement arrow. For this reason, in the intersection method, a correction amount for correcting the curve is calculated using a curve correction calculator (see Non-Patent Document 2). As a curve rectification calculator, one in which the operation of a mechanical curve rectifier is replaced with processing by a microcomputer is known (see Patent Document 1). The maintenance line engineer inputs measurement positive arrows at all measurement points in the curve to be corrected to the curve correction calculator. The measurement positive arrow is illustrated in the curve correction calculator as a positive arrow diagram. In the positive arrow diagram shown in the curve rectification calculator, the horizontal axis represents each station, and the vertical axis represents the value of the positive arrow at each station. The engineer inputs the correction amount at one measuring point to the curve calculator in order to correct the shape of the Masaya diagram. A positive arrow diagram corrected with this correction amount is calculated and shown by a curve correction calculator. The engineer inputs correction amounts at various measuring points until the positive arrow diagram shown in the curve calculator has a preferable shape. The total correction amount entered is the correction amount at each station.

  20 and 21 show the results of calculating the correction amount by using five curve rectification calculators for the same curve based on the positive arrow measured with the 10 m string. FIG. 20 is a positive arrow diagram of the curve before and after curve correction, and FIG. 21 is the correction amount of each measurement point for performing this curve correction. As shown in these figures, the amount of correction to obtain Masaya that each engineer determined to be favorable is greatly different among the engineers who calculated the amount of correction, and the calculation results will vary. Is the reality. For this reason, an unnecessarily large correction amount may be calculated, and it cannot be said that the reliability of the calculation result is high.

Japanese Utility Model Publication No. 55-126306

Susumu Kamiya “Railway Curve” Koyusha 1961 Yoshinao Kaneko's "Major arrow and curve correction" Kaneko Kogyo Kogyo Co., Ltd. 1971

  The present invention solves the above problem, and an object of the present invention is to increase the reliability of the calculation result in calculating the correction amount for correcting the curve.

  The correction amount calculation system of the present invention calculates a correction amount for curve correction on a railroad track, an input unit that receives data input, and a process that processes data input from the input unit And an output unit that outputs the data processed by the processing unit, the input unit as data, a measurement positive arrow that is a positive arrow measured at each measurement point of the measurement section including a curve, The curve length and the relaxation curve length defined for the curve are input, and the processing unit measures each measurement in the curve after correction based on the measurement arrow, the curve length, and the relaxation curve length input to the input unit. A design positive arrow calculation unit that calculates a design positive arrow that is a positive arrow of a point; and a correction amount calculation unit that calculates a correction amount of each measurement point from the design positive arrow and the measurement positive arrow. The calculation unit has the curve length and the relaxation curve length and has the front The design sum arrow is calculated such that the sum in the measurement section is equal to the sum of the measurement Masaya, and the sum of moments is equal to the sum of the moments of the measurement Masaya. The correction amount is calculated using an inverse matrix from the measurement normal arrow.

  In this correction amount calculation system, the design positive arrow calculation unit generates the design positive arrow having the curve length and the relaxation curve length, and the total sum in the measurement section is equal to the total sum of the measurement positive arrows. It is preferable to calculate the design positive arrow by adjusting the positive arrow so that the sum of moments in the measurement section becomes equal to the sum of moments of the measurement positive arrow.

  In this correction amount calculating system, the design arrow is trapezoidal in the shape of the arrow, the length of the upper base of the trapezoid is the curve length, and the length of the projected leg on the bottom is the relaxation curve length. Correspondingly, the curve length and the relaxation curve length are preferably values defined for the curve of the measurement section.

In this correction amount calculation system, n is the number of measurement points in the measurement section, MV (I) is the measurement positive arrow at the measurement point I which is the I-th (1 ≦ I ≦ n) measurement point, and DV is the design positive arrow. (I) When the correction amount is ID (I) and the column vectors having DV (I), MV (I), and ID (I) as elements are [DV], [MV], and [ID], respectively. The correction amount calculation unit generates an n-order square matrix [TR] in which the diagonal element is 1, the element adjacent to the diagonal element is −1/2, and the other elements are 0, and the inverse matrix [TR ⁻¹ is calculated, and the correction amount ID (I) at each measurement point I is preferably calculated by [ID] = [TR] ⁻¹ ([DV] − [MV]).

  In the correction amount calculation system, the processing unit further includes an error reduction unit for reducing the influence of the error of the measurement positive arrow included in the correction amount, and the error reduction unit is calculated by the correction amount calculation unit. It is preferable to remove a wavelength component more than twice as long as the extension of the measurement interval from the corrected amount.

  In the correction amount calculation system, the error reduction unit includes a high-pass filter that removes a wavelength component that is twice or more the interval extension of the measurement interval, and is based on the waveform of the correction amount calculated by the correction amount calculation unit. It is preferable that the continuous waveform is synthesized, the synthesized continuous waveform is input to the high-pass filter, and the correction amount of the measurement section is extracted from the continuous waveform output from the high-pass filter.

  The computer program for calculating a correction amount according to the present invention calculates a correction amount for curve correction on a railway track, and is a measurement that is a positive arrow measured at each measurement point in a measurement section including a curve. A design positive arrow calculation step for calculating a design positive arrow that is a positive arrow at each measurement point in the curve after correction based on the positive arrow and the curve length and relaxation curve length determined for the curve; A correction amount calculation step of calculating a correction amount of each measurement point from the arrow and the measurement positive arrow, and in the design positive arrow calculation step, the curve length and the relaxation curve length are provided, and the sum in the measurement section is included. Is calculated so that the total sum of moments is equal to the total sum of moments of the measurement positive arrows, and in the correction amount calculating step, the design positive arrow is calculated. A micro-measurement versine using an inverse matrix, wherein the correction amount is calculated.

  In the correction amount calculation computer program, the computer further executes an error reduction step for reducing the influence of the error of the measurement positive arrow included in the correction amount. In the error reduction step, the correction amount calculation step calculates the correction amount calculation step. It is preferable that a wavelength component more than twice as long as the extension of the measurement interval is removed from the corrected amount.

  According to the correction amount calculation system of the present invention, the design positive arrow calculation unit calculates the design positive arrow based on the measurement positive arrow, the curve length, and the relaxation curve length, so input the curve length and relaxation curve length of the design positive arrow. The value can be Furthermore, since the correction amount calculation unit calculates the correction amount using the inverse matrix from the design front arrow and the measurement front arrow, the correction amount for correcting the curve having such a design front arrow is obtained as the only solution. Can do. For this reason, in the calculation of the correction amount for curve correction, the reliability of the calculation result is increased.

The block block diagram of the correction amount calculation system which concerns on one Embodiment of this invention. The positive arrow figure which shows the measurement positive arrow in the same system. The figure which shows the model by the cantilever of measurement Masaya in the system. The figure which shows the model by the cantilever of the design Masaya in the same system. The flowchart of design Masaya calculation in the same system. The positive arrow figure which shows the area of the measurement positive arrow in the same system. The figure which shows the initial value of the design Masaya in the same system. The positive arrow figure which shows the gravity center of the design positive arrow and measurement positive arrow in the same system. The positive arrow figure which shows adjustment of the design positive arrow in the same system. The figure which shows the division | segmentation of the positive arrow figure for adjustment of the design positive arrow in the same system. The positive arrow figure which shows adjustment of the trapezoid part of the design positive arrow in the same system. The positive arrow figure which shows the final design positive arrow in the same system. The positive arrow figure which shows the actual example of the design positive arrow calculated with the system. The figure which shows the influence of the correction amount based on the principle of the intersection method on Masaya. The figure which shows the standard deviation of the pseudo correction amount in the said system. The figure which shows the correction amount before the error reduction in the same system, and the component removed by a high pass filter. The positive arrow figure which shows the example of the amount of positive arrows in a curve. The figure which shows the corrected amount which makes the said curve a straight line. The figure which shows the correction amount when there is no correction amount after the error reduction in the said curve, and an error. The arrow diagram of the curve before and after curve correction when the conventional curve correction calculator is used. The figure which shows the calculation result of the corrected amount in the same curve correction.

  A correction amount calculation system according to an embodiment of the present invention will be described with reference to FIGS. The correction amount calculation system 1 calculates a correction amount for curve correction on a railway track, and includes an input unit 2, a processing unit 3, and an output unit 4 as shown in FIG. . The input unit 2 receives data input. The processing unit 3 processes the data input from the input unit 2. The output unit 4 outputs the data processed by the processing unit 3.

  The correction amount calculation system 1 includes a computer as hardware and a computer program for correction amount calculation as software. In this embodiment, a notebook personal computer (notebook PC) is used as the computer. The input unit 2 is a computer input device, for example, a keyboard and a mouse. The processing unit 3 is a computer processing device, and includes a CPU that executes a computer program and a memory that stores the computer program and data. In the present embodiment, a notebook PC display and printer are used as the output unit 4.

  As shown in FIG. 2, the measurement unit MV, the curve length CL, and the relaxation curve lengths TCL1 and TCL2 are input to the input unit 2 as data. The measurement positive arrow MV is a positive arrow measured at each measurement point I in the measurement section including the curve. The curve length CL is the length of the circular curve in the curve. The relaxation curve lengths TCL1, TCL2 are the lengths of the relaxation curves connected to the start and end of the circular curve. The section extension TL of the measurement section is the sum of the curve length CL, the relaxation curve lengths TCL1 and TCL2, and the lengths L1 and L2 of the straight section. Although the straight arrow on the straight line is 0, FIG. 2 shows a case where the straight line section has a slight amount of positive arrow.

  The processing unit 3 includes a design positive arrow calculation unit 31, a correction amount calculation unit 32, and an error reduction unit 33 (see FIG. 1). The design Masaya calculation unit 31 is a functional part realized by the processing unit 3 executing the design Masaya calculation step of the correction amount calculation computer program. The correction amount calculation unit 32 is a functional part realized by the processing unit 3 executing the correction amount calculation step of the correction amount calculation computer program. The design positive arrow calculation unit 31 calculates the design positive arrow DV based on the measurement positive arrow MV, the curve length CL, and the relaxation curve lengths TCL1 and TCL2 input to the input unit 2. Design positive arrow DV is a positive arrow of each measuring point I in the curve after correction. The correction amount calculation unit 32 calculates the correction amount of each measurement point using the inverse matrix from the design positive arrow DV and the measurement positive arrow MV.

  The output unit 4 outputs the correction amount calculated by the processing unit 3. In the present embodiment, the measurement positive arrow MV and the design positive arrow DV are displayed on the display as the output unit 4 together with the correction amount of each measurement point.

  The processing in the processing unit 3 will be further described in detail. Here, the number of measurement points in the measurement section is n, the measurement arrow at the measurement point I which is the I-th (1 ≦ I ≦ n) measurement point is MV (I), and the design positive arrow is DV (I). (See FIG. 2). Let L (I) be the distance from a predetermined point to the measuring point I in the diagram. The predetermined point is, for example, the first measurement point. Since the intervals between the measurement points are equal, the distance in the arrow diagram may be L (I) = I.

  The design Masaya calculation unit 31 includes the curve length CL and the relaxation curve lengths TCL1 and TCL2 input to the input unit 2, and is represented by a measurement section (station 1 to station n) as represented by Equation 1. The total sum of the design positive arrows DV (I) in FIG. 5 is equal to the total sum of the measurement positive arrows MV (I) and, as expressed by Equation 2, the moment of the design positive arrows DV (I) × L (I) The design positive arrow DV (I) is calculated so that the total sum becomes equal to the total sum of moments MV (I) × L (I) of the measurement positive arrow. The moment is a geometric moment in the Masaya diagram.

  The condition expressed by Equation 1 means that the angle formed by the start and end tangents of the curve is the same for both curves before and after correction, that is, the curve does not break at both ends (see Non-Patent Document 1). The condition expressed by Equation 2 means that both ends of the curve after correction are on the tangent line at the beginning and end of the curve before correction, that is, the curves do not collide before and after correction (Non-Patent Document 1). reference).

  The conditions expressed by Equation 1 and Equation 2 are modeled as cantilever beams as shown in FIGS. In FIG. 3, the load MV (I) is applied to the cantilever 5 at a point away from the support point by a distance L (I). The moment applied to the cantilever 5 by the load MV (I) is MV (I) × L (I). In FIG. 4, the load DV (I) is applied to the cantilever 5 at a point away from the support point by a distance L (I). The moment applied to the cantilever 5 by the load DV (I) is DV (I) × L (I).

  Here, a column vector having MV (I) as an element is [MV], and a column vector having DV (I) as an element is [DV]. In this model, [MV] and [DV] are treated as distributed loads on the cantilever beam 5, and the fulcrum reaction force and support point moment by [MV] are equivalent to the fulcrum reaction force and support point moment by [DV]. [DV] is calculated from the following conditions. The support point reaction force is the sum of loads applied to the cantilever 5. The support point moment is the sum of moments applied to the cantilever beam 5.

  The design positive arrow DV has a trapezoidal shape of the positive arrow (the shape of the positive arrow diagram), the length of the upper base of the trapezoid is the curve length CL, and the length of the projection of the leg on the lower base is the relaxation curve lengths TCL1, TCL2. Correspond to each. The curve length CL and the relaxation curve lengths TCL1 and TCL2 are administratively defined values for the curves in the measurement section, that is, defined values (management values). When the curve radius (radius of the circular curve) is given, the specified value of the curve length CL is determined from the intersection angle, and the specified values of the relaxation curve lengths TCL1 and TCL2 are determined from the rules. The intersection angle is the same size as the central angle of the circular curve (arc).

  The positive arrow shape of the measurement positive arrow MV has irregularities due to traversing. If the design positive arrow DV is calculated from only the measurement positive arrow MV by removing the irregularities by a moving average method or a simple filter calculation, the positive arrow shape of the design positive arrow DV has a specified value. It may change significantly from shape.

  Moreover, if the design positive arrow DV is calculated only from the prescribed values of the curve length CL and the relaxation curve lengths TCL1, TCL2, the calculated design arrow DV may not match the field curve. For example, in most cases, the curve radii of the upper and lower lines in the double-line section of the conventional line are set to the same value by using the curve radius of the line center line. However, precisely, the actual curve radius of the upper and lower lines is different. Furthermore, the straight section before and after the curve often has a slight amount of positive arrows (about 3000 m to 10000 m in terms of the curve radius).

  The correction amount calculation system 1 of the present embodiment calculates the design positive arrow DV based on the measurement positive arrow MV, the curve length CL, and the relaxation curve lengths TCL1 and TCL2. The calculation of the design positive arrow DV in the correction amount calculation system 1 will be described in detail. As shown in FIG. 5, the curve length CL and the relaxation curve lengths TCL1 and TCL2 are input from the input unit 2 (step S101).

  Next, a measurement positive arrow MV is input from the input unit 2 (step S102).

  Next, the design positive arrow calculation unit 31 of the processing unit 3 generates an initial value of the design positive arrow DV (step S103). The initial value of the design Masaya DV has the input curve length CL and relaxation curve lengths TCL1, TCL2, and the sum of DV in the measurement section is equal to the sum of the measurement Masaya MV.

  The arithmetic processing in the design positive arrow calculation part 31 is demonstrated using a positive arrow figure. As shown in FIG. 6, the area of the positive arrow diagram of the measurement positive arrow MV in the measurement section (the hatched portion) is calculated. This area is a value obtained by multiplying the total ΣMV (I) for all measurement points (I = 1 to n) of the measurement positive arrow MV (I) at the measurement point I by the interval of the measurement points. Since the interval between the measurement points is constant, the calculation of the area can be simplified by setting the interval between the measurement points to 1. The area of the positive arrow is the magnitude of the reaction force at the support point in the cantilever model. As shown in FIG. 7, a design positive arrow DV in which the area of the positive arrow figure is equal to the area of the positive arrow figure of the measurement positive arrow MV is generated. This design positive arrow DV is a trapezoid, and the length of the upper base of the trapezoid corresponds to the curve length CL, and the length obtained by projecting the trapezoidal leg to the lower base corresponds to the relaxation curve lengths TCL1 and TCL2. The trapezoidal height h is calculated by the following equation. Σ represents the total sum of all measurement points (I = 1 to n).

  h = ΣMV (I) / {(TCL1 + TCL2) / 2 + CL}

  Next, the generated design positive arrow DV is adjusted so that the sum of the moments of DV in the measurement section becomes equal to the sum of moments of the measurement positive arrow MV. The sum of moments is the moment of support point in the cantilever model. As shown in FIG. 8, the design positive arrow DV is superimposed on the measurement positive arrow MV so that the center of gravity position G in the horizontal direction (X direction) in the positive arrow figure coincides (step S104 in FIG. 5). The gravity center position G of the measurement arrow MV is calculated by the following equation.

  G = (ΣMV (I) × L (I)) / (ΣMV (I))

  The center of gravity position G of the design positive arrow DV is calculated as a trapezoidal geometric center of gravity.

  The design positive arrow DV (I) at each measurement point I is the size of the trapezoidal vertical direction (Y direction) at the measurement point I. By combining the center of gravity position G, the total sum of moments of the design positive arrow DV becomes equal to the total sum of moments of the measurement positive arrow MV, as represented by the following equation.

  ΣDV (I) × L (I) = ΣMV (I) × L (I)

  However, when the measurement arrow MV is not 0 at the end point of the measurement section, the design arrow DV and the measurement arrow MV do not match at the measurement point. In this case, the upper and lower bases of the design arrow (trapezoid) of the design positive arrow DV are moved up and down to measure the design positive arrow DV at the start and end points without changing the area of the positive arrow figure. Match with Masaya MV (step S105 in FIG. 5). Mathematically precise accuracy is not required, and it may be adjusted with sufficient accuracy in track maintenance.

  As shown in FIG. 9, when the lower base of the trapezoid is moved in the Y direction by Ys, and a constant value Ys is added to all design positive arrows in the measurement section, the area S1 of the positive arrow diagram by Ys is expressed by the following equation: It is represented by

  S1 = (L1 + TCL1 + CL + TCL2 + L2) × Ys

  The upper base of the trapezoid is moved by Δh in the Y direction so that the area of the design positive arrow DV does not change. If the trapezoidal area at that time is S2, the area S2 is expressed by the following equation.

  S2 = {(TCL1 + TCL2) / 2 + CL} × (h−Ys−Δh)

  Δh is calculated so that the area (S1 + S2) of the design positive arrow DV is equal to ΣMV (I).

  Next, Ys, which is the design positive arrow DV at the measurement point at the start of the measurement section, is changed, and the design correction when the difference between the sum of the moments of the design positive arrow DV and the measurement positive arrow MV is minimized. The arrow DV is calculated. The difference between the sum of moments of the design Masaya DV and the sum of moments of the measurement Masaya MV is expressed by the following equation.

  | ΣDV (I) × L (I) −ΣMV (I) × L (I) |

  The design positive arrow when the difference between the sum of moments of the design positive arrow DV and the sum of moments of the measurement positive arrow MV is minimized is defined as DVS. The design positive arrow DVS changes the center of gravity position from the measurement positive arrow MV by changing Ys from 0. For this reason, the design Masaya DVS is readjusted as follows.

  As shown in FIG. 10, the design positive arrow DVS is divided into a base portion DVSb and a trapezoidal portion DVSd, and the measurement positive arrow MV and the design positive arrow DVS are moved in the Y direction by −Ys. The base portion DVSb is a rectangle having a constant height Ys in the measurement section. By this movement, the positive arrow diagram of the measurement positive arrow becomes MV-Ys, and the base of the trapezoidal portion DVSd is in contact with the X axis.

  Next, as shown in FIG. 11, the trapezoidal portion DVSd is moved in the left or right direction (X direction), and the barycentric position of the trapezoidal part DVSd is matched with the barycentric position of the measurement positive arrow MV-Ys. The base portion DVSb does not move. Due to the movement of the trapezoidal portion DVSd, the curve length CL and the relaxation curve lengths TCL1, TCL2 do not change. The lengths L1 and L2 of the straight section change, but the total length L1 + L2 of the straight section does not change. Finally, the base portion DVSb and the trapezoidal portion DVSd are moved in the Y direction by + Ys. Note that the movement of the graphic as described above is a description of the calculation process in the design Masaya calculation unit 31 with reference to the drawing, and no drawing is required in the calculation process.

  As described above, the design positive arrow DV is adjusted by the design positive arrow calculation unit 31, and the final design positive arrow DV (DVS) as shown in FIG. 12 is calculated. The final design positive arrow DV is output to the output unit 4 and the correction amount calculation unit 32 (step S106).

  For an actual curve, a measurement Masaya MV, a design Masaya DV (30 m moving average method) calculated by a conventional curve correction calculator, and a design Masaya DV (one piece calculated by the correction amount calculation system 1 of the present embodiment) FIG. 13 shows the holding beam calculation method. One relaxation curve length TCL1 in the curve is 30 m, and the other relaxation curve length TCL2 is 25 m. In the conventional 30 m moving average method, it is difficult to maintain the basic alignment of the curve, particularly the relaxation curve. On the other hand, in the correction amount calculation system 1, the curve length CL and the relaxation curve lengths TCL1, TCL2 of the design positive arrow DV can be set to input values, and the design positive arrow DV in the circular curve can be made constant. It was confirmed that

  Next, calculation of the correction amount will be described in detail. First, the influence of the correction amount based on the principle of the intersection method on Masaya will be described. Let MV (I) be the measurement arrow at the measurement point I, and ID (I) be the correction amount. As shown in FIG. 14, when the correction amount S is given to the measuring point I, the positive arrow at the measuring point I increases by S to become MV (I) + S, and the positive arrows at the adjacent measuring points I-1, I + 1. The arrow decreases by S / 2 to M (I-1) -S / 2 and M (I + 1) -S / 2. Thus, the correction amount ID (I) at each station I changes the arrow at the station and the arrow at the adjacent station.

  In the present embodiment, the correction amount ID (I) is given to each measurement point I (I = 1 to n), and the measurement positive arrow MV (I) becomes the design positive arrow DV (I) that is a predetermined design value. Like that. When a matrix is used, such a design positive arrow DV (I) is represented by the following expression based on the principle of the intersection method described above.

  An n-order square matrix on the right side of Equation 3 is [TR], and an element in I row and I column of [TR] is TR (I, J). In the matrix [TR], the diagonal element TR (I, I) is 1, the elements TR (I, I-1) and TR (I, I + 1) adjacent to the diagonal element are -1/2, and other elements Is 0. The matrix [TR] is a real symmetric matrix. When a 10 m string is used for the measurement of Masaya, the matrix [TR] may be represented as [TR10].

  Assuming that the column vectors whose elements are the design positive arrow DV (I), the measurement positive arrow MV (I), and the correction amount ID (I) are [DV], [MV], and [ID], respectively, It is expressed by a formula.

(Formula 4)
[DV] = [MV] + [TR] [ID]

Since the matrix [TR] is determinant det [TR] ≠ 0, the inverse matrix [TR] ⁻¹ exists. Therefore, the correction amount [ID] is calculated by the following equation.

(Formula 5)
[ID] = [TR] ⁻¹ ([DV] − [MV])

In the correction amount calculation unit 32, the diagonal element TR (I, I) is 1, the elements TR (I, I-1) and TR (I, I + 1) adjacent to the diagonal element are -1/2, and the others An nth-order square matrix [TR] whose elements are 0 is generated, and its inverse matrix [TR] ⁻¹ is calculated. The correction amount calculation unit 32 calculates the correction amount ID (I) at each measurement point I by [ID] = [TR] ⁻¹ ([DV] − [MV]). The inventors of the present application have devised using a matrix or an inverse matrix for calculating the correction amount.

For example, when a 10 m string is used and the number of measurement points is 5, [TR10] is a quartic square matrix, and the determinant det [TR10] = 3/16 ≠ 0. The inverse matrix [TR10] ⁻¹ is obtained by the Gauss-Jordan method as follows.

Thus, according to the correction amount calculation system 1 of the present embodiment, the design positive arrow calculation unit 31 calculates the design positive arrow DV based on the measurement positive arrow MV, the curve length CL, and the relaxation curve lengths TCL1, TCL2. The curve length CL and the relaxation curve lengths TCL1 and TCL2 of the design positive arrow DV can be set to input values. The value to be entered is a value specified for the curve. In addition, the design positive arrow DV in the circular curve can be made constant. Furthermore, since the correction amount calculation unit 32 calculates the correction amount ID from the design positive arrow DV and the measurement positive arrow MV using the inverse matrix [TR] ⁻¹ , the correction amount calculation unit 32 corrects the curve having the design positive arrow DV. The correction amount ID can be obtained as the only solution. For this reason, in the calculation of the correction amount ID for curve correction, the reliability of the calculation result is increased.

  By the way, the calculated correction amount ID includes the influence of the error of the measurement Masaya MV. Assuming that the error of measurement Masaya [MV] is a white error that occurs regardless of numerical values before and after the measurement, linear conditions, etc., the measurement Masaya [MV] is expressed by the following equation. The true value part [MVr] of the measurement positive arrow and the error part [MVe] of the measurement positive arrow are considered to be superimposed.

(Formula 7)
[MV] = [MVr] + [MVe]

  When this [MV] is substituted into Equation 5, the correction amount [ID] is calculated by the following equation.

(Formula 8)
[ID] = [TR] ⁻¹ ([DV] − [MVr] − [MVe])

  Of the correction amount [ID], the influence [IDe] of the error [MVe] of the measurement positive arrow is expressed by the following equation. This [IDe] is called a pseudo correction amount.

(Formula 9)
[IDe] = − [TR] ⁻¹ [MVe]

  The error [MVe] of the measurement positive arrow is a random value with an average value = 0 and a standard deviation σ. σ varies depending on the accuracy of the measuring means. The standard deviation σ is about 0.3 mm to 0.5 mm in the track inspection vehicle (based on 10 m Masaya Masaya) at West Japan Railway Company. The standard deviation σ is about 0.8 mm to 1.5 mm in the 10-meter string Masaya hand measurement (yarn string).

If the scalar elements of the pseudo correction amount [IDe] and the error [MVe] of the measurement positive arrow are ide (I) and mve (I), respectively, the variance σ ² _{{ide (I )}} Is expressed as the following equation.

Here, if σ {mve (i)} = ε (ε≈0.3 mm to 0.5 mm), the standard deviation σ _{{ide (I)}} of the pseudo correction amount is expressed as the following equation.

According to Equation 11, σ of each term of [IDe] is amplified more than σ of each term of [MVe]. Moreover, amplification of the standard deviation σ _{{ide (I)}} of the pseudo correction amount is promoted as the number of measurement points n increases.

Conventionally, the crossing method is theoretically a method that can calculate the actual line shape, but it is considered that it cannot be used if it exceeds a certain extension. The fact that the standard deviation σ _{{ide (I)} of the} pseudo correction amount is promoted as the number of measurement points n is increased leads to such a past consideration.

  When the standard deviation of each term of the error sequence [MVe] in the measurement correct arrow [MV] is ε, the standard deviation α (i) of the i row element ide (i) of the generated pseudo correction amount [IDe] Is expressed by the following equation from Equation 9.

  Where mve (1) = mve (i) = mve (n)

  From Equation 11, the standard deviation α (i) is expressed by the following equation.

On the other hand, [TR10] ⁻¹ is an n × n matrix. Its elements are point symmetric and satisfy the following equation.

  Therefore, the following equation is derived.

  The standard deviation α (i) possessed by ide (i) and the standard deviation α (n + 1-i) possessed by ide (n + 1-i) have a relationship represented by the following expression.

(Formula 16)
α (i) = α (n + 1−i)

  As shown in FIG. 15, if the vertical axis is the standard deviation α (i) and the horizontal axis is the number of each element of [IDe], the standard deviation α (i) appears symmetrically according to the relationship of Equation 16. To do. α (i) increases with the interval extension TL of the measurement interval, that is, with the number of rows of [IDe], and σ {ide (25)} in the central portion ide (25) when [IDe] is 50 rows. Approximately 9.7mm. The standard deviation α (i) is considered to appear with a certain probability of occurrence in a shape in which the section extension TL of the measurement section is a half wavelength. For this reason, the correction amount is removed from the correction amount ID calculated based on the measurement arrow MV including the measurement error by a high-pass filter (HPF) by removing a wavelength component more than twice the section extension TL (2TL). The influence of measurement error on ID is reduced.

  In the correction amount calculation system 1 of the present embodiment, the processing unit 3 includes an error reduction unit 33 for reducing the influence of the error of the measurement positive arrow MV included in the correction amount ID (see FIG. 1). The error reduction unit 33 is a functional part realized by the processing unit 3 executing the error reduction step of the correction amount calculation computer program. The error reduction unit 33 removes a wavelength component that is twice or more the interval extension TL of the measurement interval from the correction amount ID calculated by the correction amount calculation unit 32.

  The error reduction will be further described in detail. The error reduction unit 33 includes a high-pass filter (HPF) 331 that removes a wavelength component that is twice or more the section extension TL of the measurement section. The high pass filter 331 is a digital filter realized by digital processing of the processing unit 3. As shown in FIG. 16, the correction amount ID calculated by the correction amount calculation unit 32 is obtained for the measurement section of the section extension TL. The error reduction unit 33 connects the same waveform inverted up and down before and after the calculated correction amount ID waveform. A continuous waveform based on the waveform of the correction amount ID is synthesized by repeatedly connecting the correction amount ID waveform upside down. The error reduction unit 33 inputs the synthesized continuous waveform to the high pass filter 331 and extracts the correction amount of the measurement section from the continuous waveform output from the high pass filter 331. As a result, a wavelength component that is twice or more the section extension TL of the measurement section is removed from the correction amount ID calculated by the correction amount calculation unit 32.

  The validity of the above error reduction is confirmed based on the data. In Equation 5, if [DV] = [0] (zero vector), the following equation is obtained.

(Formula 17)
[ID] =-[TR] ^-1 [MV]

  The correction amount [ID] calculated by Expression 17 is a correction amount for making a curve having a positive arrow amount [MV] into a straight line ([DV] = [0]). It becomes a real linear.

  For example, if the amount of positive arrows shown in FIG. 17 is substituted for [MV] in Equation 17, the correction amount [ID] shown in FIG. 18 is obtained. The correctness of the correction amount [ID] is confirmed by inverting the sign of the correction amount [ID] so as to match the linear shape of the curve. This is the amount of correction when there is no error in the measurement arrow.

  The correction amount [ID] shown in the center part of FIG. 16 is a measurement positive arrow obtained by superposing a white error (average m = 0, standard deviation σ = 0.5 mm) on the positive arrow amount [MV] shown in FIG. It is obtained by substituting into Equation 17. FIG. 19 shows a correction amount (correction amount after HPF removal) obtained by removing a wavelength component more than twice the interval extension TL of the measurement interval from the correction amount [ID]. This figure shows the correction amount (correct correction amount) when there is no error in the measurement positive arrow, along with the correction amount after HPF removal. The correction amount after HPF removal is not completely coincident with the correction amount (correct correction amount) when there is no error in the measurement positive arrow, but it was confirmed that a numerical value having no practical problem can be obtained.

  As described above, according to the correction amount calculation system 1 of the present embodiment, the error reduction unit 33 removes a wavelength component that is twice or more the interval extension TL of the measurement interval from the correction amount ID calculated by the correction amount calculation unit 32. By doing so, the influence of the measurement error of the measurement arrow MV can be reduced. Even in a curve having a long measurement section extension TL and a large number of measurement points, a correction amount with a small error can be calculated, and the reliability of the calculation result is ensured.

  In addition, this invention is not restricted to the structure of said embodiment, A various deformation | transformation is possible in the range which does not change the summary of invention. For example, the string in the measurement of Masaya is not limited to 10 m, and may be 20 m or 40 m, for example.

DESCRIPTION OF SYMBOLS 1 Correction amount calculation system 2 Input part 3 Processing part 31 Design positive arrow calculation part 32 Correction amount calculation part 33 Error reduction part 331 High pass filter 4 Output part CL Curve length DV Design positive arrow ID Correction amount TL Section extension MV measurement Masaya TCL1, TCL2 Relaxation curve length

Claims (8)

A correction amount calculation system for calculating a correction amount for curve correction in a railway track,
An input unit for receiving data; and
A processing unit for processing data input from the input unit;
An output unit that outputs data processed by the processing unit,
The input unit, as data, a measurement arrow that is a positive arrow measured at each measurement point of a measurement section including a curve, and a curve length and a relaxation curve length determined for the curve are input,
The processing unit is a design positive arrow calculation unit that calculates a design positive arrow that is a positive arrow of each measurement point in the curve after correction based on the measurement positive arrow, the curve length, and the relaxation curve length input to the input unit And a correction amount calculation unit for calculating the correction amount of each measurement point from the design positive arrow and the measurement positive arrow,
The design Masaya calculation unit has the curve length and the relaxation curve length, and the sum in the measurement section is equal to the sum of the measurement Masaya, and the sum of moments is equal to the sum of the moments of the measurement Masaya. Calculate design Masaya,
The correction amount calculation unit, wherein the correction amount calculation unit calculates the correction amount using an inverse matrix from the design front arrow and the measurement front arrow.   The design positive arrow calculation unit has the curve length and the relaxation curve length and generates a design positive arrow in which the total sum in the measurement interval is equal to the total sum of the measurement positive arrows, and the generated design positive arrow in the measurement interval. The correction amount calculation system according to claim 1, wherein the design positive arrow is calculated by adjusting the sum of moments to be equal to the total sum of moments of the measurement positive arrow. The design positive arrow has a trapezoidal shape, and the length of the upper base of the trapezoid corresponds to the curve length, and the length of the projected leg on the lower base corresponds to the relaxation curve length.
The correction amount calculation system according to claim 2, wherein the curve length and the relaxation curve length are values defined for the curve of the measurement section. The number of measurement points in the measurement section is n, the measurement arrow at the measurement point I which is the I-th (1 ≦ I ≦ n) measurement point is MV (I), the design positive arrow is DV (I), and the correction amount is ID (I)
If the column vectors whose elements are DV (I), MV (I) and ID (I) are [DV], [MV] and [ID], respectively,
The correction amount calculation unit generates an n-order square matrix [TR] in which the diagonal element is 1, the element adjacent to the diagonal element is −1/2, and the other elements are 0, and the inverse matrix [TR ^-1 is calculated, and the correction amount ID (I) at each measurement point I is calculated by [ID] = [TR] ^-1 ([DV]-[MV]). The correction amount calculation system according to any one of items 3 to 4. The processing unit further includes an error reduction unit for reducing the influence of measurement error arrow included in the correction amount,
5. The error reduction unit removes a wavelength component that is at least twice as long as an extension of the measurement interval from the correction amount calculated by the correction amount calculation unit. The correction amount calculation system according to item.   The error reduction unit includes a high-pass filter that removes a wavelength component that is twice or more the interval extension of the measurement interval, and synthesizes a continuous waveform based on the waveform of the correction amount calculated by the correction amount calculation unit, 6. The correction amount calculation system according to claim 5, wherein the synthesized continuous waveform is input to the high-pass filter, and the correction amount of the measurement section is extracted from the continuous waveform output from the high-pass filter. A computer program for calculating a correction amount for calculating a correction amount for curve correction in a railway track,
Based on the measurement arrow that is the positive arrow measured at each station in the measurement section including the curve, and the curve length and relaxation curve length determined for the curve, A design positive arrow calculation step for calculating a design positive arrow that is an arrow;
A correction amount calculating step for calculating a correction amount for each measurement point from the design positive arrow and the measurement positive arrow is executed by a computer,
In the design positive arrow calculation step, the curve length and the relaxation curve length are provided, the sum in the measurement section is equal to the total sum of the measurement positive arrows, and the sum of moments is equal to the total sum of moments of the measurement positive arrows. Design Masaya is calculated in
In the correction amount calculating step, the correction amount is calculated from the design front arrow and the measurement front arrow using an inverse matrix. Further causing the computer to perform an error reduction step for reducing the influence of the error of the measurement positive arrow included in the correction amount;
8. The correction amount calculation according to claim 7, wherein, in the error reduction step, a wavelength component that is twice or more as long as an extension of the measurement interval is removed from the correction amount calculated in the correction amount calculation step. Computer program.

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