JP2020186546A - Track displacement forecast method and track displacement forecasting system - Google Patents

Abstract

To provide a track displacement forecast method which can forecast future track displacement with high accuracy even if historical track displacement data are limited and insufficient.SOLUTION: Based on a calculated value CV1 of an index IN1 indicating the variation of track displacement measured the first time and a calculated value CV2 of the index IN1 indicating the variation of track displacement measured the second time, an index IN2 that shows the degree of change in track displacement before the second measurement is calculated, and a regression equation RE1 that shows the relationship between the index IN1 and the index IN2 is calculated, and based on a forecast value PV1 of the index IN2 calculated based on the regression equation RE1 and the calculated value CV4 of a correction coefficient CF1 which shows the relationship with the calculated value CV3 of the index IN2, the index IN3, which indicates the degree of change in track displacement after the second measurement is forecast.SELECTED DRAWING: Figure 6

Description

The present invention relates to a track displacement prediction method and a track displacement prediction system for predicting track displacement.

As a method of predicting future track displacement from measurement data of track displacement in tracks such as railroad tracks, track displacement has been measured from the past, and when track displacement history data can be sufficiently secured, track displacement A method of predicting future orbital displacement by data processing based on historical data and a method of improving the accuracy of prediction by reflecting newly obtained orbital displacement data are known.

Here, the track displacement is the difference between the high-low displacement, which is the vertical displacement of the rail, the street displacement, which is the displacement in the width direction (left-right direction) of the rail, and the set value of the distance between the rails on both the left and right sides. It is possible to exemplify the inter-track displacement, the level displacement which is the difference from the set value of the height difference between the left and right rails, and the flat displacement which is the level difference between two points separated by a certain distance. it can.

Japanese Patent Application Laid-Open No. 2018-76724 (Patent Document 1) describes a method for determining sequential update prediction of time-series data obtained by measuring a predetermined orbital inspection section based on newly acquired time-series data. A technique is disclosed in which the posterior distribution is calculated and compared with the rate of change of the posterior distribution result one or more times before and the rate of change of the posterior distribution based on newly acquired data.

Japanese Patent Application Laid-Open No. 2018-76681 (Patent Document 2) describes a step of predicting a future transition of orbital displacement based on historical data of orbital displacement in an orbital maintenance management method, and a reference value of the predicted orbital displacement. The process of selecting a location that exceeds the maintenance target location, the process of determining the risk of a location where the predicted track displacement does not exceed the reference value, and the process of determining the risk of the location where the determined risk exceeds the threshold value, the predicted track displacement is the reference value. A technique including a process of selecting a location that does not exceed the above as a location to be maintained is disclosed.

Japanese Patent Application Laid-Open No. 2017-110375 (Patent Document 3) describes a measurement data acquisition unit that acquires track measurement data in a track correction procedure generator, and a travel simulation that simulates track travel by a vehicle. It is provided with a simulation execution unit that performs a simulation based on a speed determined according to the position of the vehicle in the vehicle, and a correction procedure generation unit that generates a correction procedure that is information indicating the correction content of the track based on the result of a running simulation. The technology is disclosed.

JP-A-2018-76724 JP-A-2018-76681 Japanese Unexamined Patent Publication No. 2017-10375

In the conventional method of predicting orbital displacement, when the historical data of orbital displacement acquired in the past is sufficiently accumulated, the orbital displacement is predicted based on the accumulated data. However, when the historical data of the orbital displacement is not sufficiently accumulated, it is difficult to predict the orbital displacement with high accuracy.

The present invention has been made to solve the above-mentioned problems of the prior art, and even if the historical data of the orbital displacement is small and insufficient in the orbital displacement prediction method for predicting the orbital displacement, the future It is an object of the present invention to provide an orbital displacement prediction method capable of predicting orbital displacement with high accuracy.

A brief outline of the typical inventions disclosed in the present application is as follows.

The orbital displacement prediction method as one aspect of the present invention is an orbital displacement prediction method for predicting the orbital displacement in each of a plurality of sections in an orbit including a plurality of sections arranged along the length direction of the orbit. The orbital displacement prediction method measures orbital displacement at a plurality of measurement positions different from each other along the length direction in each of a plurality of sections, and measures a plurality of orbital displacements measured at each of the plurality of measurement positions. After measuring the orbital displacement in steps (a) and (a) for calculating the first index representing the variation in the values, the orbital displacement is measured again at a plurality of measurement positions in each of the plurality of sections, and the first It has (b) a step of recalculating one index. Further, in the orbital displacement prediction method, the first calculated value of the first index calculated in the step (a) and the second index of the first index calculated in the step (b) are used in each of the plurality of sections. Based on the calculated value, the second index indicating the degree of change in the orbital displacement before measuring the orbital displacement in step (b) is calculated in step (c), and each of the plurality of sections is calculated. The first index and the second index are based on the plurality of first calculated values and the third calculated value of the plurality of second indexes calculated in each of the plurality of sections in the step (c). It has (d) step of calculating a regression equation showing a relationship. Further, in the orbital displacement prediction method, the first predicted value of the second index is calculated based on the first calculated value and the regression equation in each of the plurality of sections, and the calculated first predicted value is used. , The second calculated value, the regression equation, and the step (e) were calculated in the step (e) for calculating the first correction coefficient indicating the relationship between the third calculated value and the third calculated value, and in each of the plurality of sections. Based on the 4th calculated value of the 1st correction coefficient, the 2nd predicted value of the 3rd index showing the degree of change in the orbital displacement after the orbital displacement is measured in the step (b) is calculated (f). Has steps and.

Further, as another aspect, in the step (e), the first predicted value is calculated and calculated by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections. The first correction coefficient, which is the ratio of the third calculated value to the one predicted value, may be calculated.

Further, as another aspect, in the step (f), the third predicted value of the second index is calculated by substituting the second calculated value as the first index into the regression equation in each of the plurality of sections. The second predicted value may be calculated by multiplying the calculated third predicted value by the first correction coefficient.

Further, as another aspect, in the orbital displacement prediction method, after the orbital displacement is measured in step (b), the orbital displacement is measured again at a plurality of measurement positions in each of the plurality of sections, and the first index is used. In the (g) step, which is calculated again, and in each of the plurality of sections, the (g) step is based on the second calculated value and the fifth calculated value of the first index calculated in the (g) step. It may have a step (h) of calculating a fourth index indicating the degree of change in the orbital displacement before measuring the orbital displacement in. In addition, the orbital displacement prediction method determines the relationship between the third predicted value, the sixth calculated value of the fourth index calculated in step (h), and the first correction coefficient in each of the plurality of sections. The fifth calculated value, the regression equation, the fourth calculated value, and the second correction coefficient calculated in the (i) step in each of the step (i) and the plurality of sections for calculating the second correction coefficient shown. Based on the 7th calculated value of (g), the 4th predicted value of the 5th index indicating the degree of change in the orbital displacement after the orbital displacement was measured in the (g) step is calculated (j). You may have.

Further, as another aspect, in the step (i), the second correction coefficient, which is the ratio of the sixth calculated value to the product of the third predicted value and the first correction coefficient, is calculated in each of the plurality of sections. You may.

Further, as another aspect, in the step (e), the first predicted value is calculated and calculated by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections. The first correction coefficient, which is the difference between the first predicted value and the third calculated value, may be calculated.

The orbital displacement prediction method as one aspect of the present invention is an orbital displacement prediction method for predicting the orbital displacement in each of a plurality of sections in an orbit including a plurality of sections arranged along the length direction of the orbit. The orbital displacement prediction method measures orbital displacement at a plurality of measurement positions different from each other along the length direction in each of a plurality of sections, and measures a plurality of orbital displacements measured at each of the plurality of measurement positions. Based on the values, the first index representing the variation of the measured values of the plurality of track displacements and the second index representing the wheel load or the rail pressure in each of the plurality of sections are calculated (a), and (a). a) After measuring the orbital displacement in the step, the orbital displacement is measured again at a plurality of measurement positions in each of the plurality of sections, and the first index and the second index are recalculated (b). Have. Further, in the orbital displacement prediction method, the first calculated value of the first index calculated in the step (a) and the second index of the first index calculated in the step (b) are used in each of the plurality of sections. Based on the calculated value, a third index indicating the degree of change in the orbital displacement before measuring the orbital displacement in the step (b) is calculated (c) and a plurality of sections in the step (a). Based on the first index calculated value of the plurality of second indexes calculated in each of the above and the third calculated value of the plurality of third indexes calculated in each of the plurality of sections in step (c). The step (d) is to calculate a regression equation showing the relationship between the second index and the third index. In addition, the orbital displacement prediction method calculates the first predicted value of the third index based on the first index calculated value and the regression equation in each of the plurality of sections, and the calculated first predicted value. The second index calculated value of the second index calculated in the step (e) for calculating the first correction coefficient indicating the relationship between the third calculated value and the third calculated value, and in the step (b) for each of the plurality of sections. Based on the regression equation and the fourth calculated value of the first correction coefficient calculated in step (e), the degree of change in orbital displacement after measuring the orbital displacement in step (b) is determined. It has (f) step of calculating the second predicted value of the fourth index to represent.

The orbital displacement prediction system as one aspect of the present invention is an orbital displacement prediction system that predicts the orbital displacement in each of a plurality of sections in an orbit including a plurality of sections arranged along the length direction of the orbit. The orbital displacement prediction system measures the orbital displacement at a plurality of measurement positions different from each other along the length direction in each of a plurality of sections, and measures a plurality of orbital displacements measured at each of the plurality of measurement positions. After the orbital displacement is measured by the first calculation unit that calculates the first index representing the variation of the value and the first calculation unit, the orbital displacement is measured again at a plurality of measurement positions in each of the plurality of sections, and the first It has a second calculation unit that calculates one index again. In addition, the track displacement prediction system has a first calculated value of the first index calculated by the first calculation unit and a second calculated value of the first index calculated by the second calculation unit in each of the plurality of sections. Based on the above, the third calculation unit that calculates the second index indicating the degree of change in the orbital displacement before the orbital displacement is measured by the second calculation unit, and the plurality calculated in each of the plurality of sections. The relationship between the first index and the second index is shown based on the first calculated value of the above and the third calculated value of the plurality of second indexes calculated by the third calculation unit in each of the plurality of sections. It has a fourth calculation unit for calculating a regression equation. Further, the orbital displacement prediction system calculates the first predicted value of the second index based on the first calculated value and the regression equation in each of the plurality of sections, and uses the calculated first predicted value. , The fifth calculation unit that calculates the first correction coefficient indicating the relationship with the third calculation value, and the second calculation value, the regression equation, and the fifth calculation unit calculated by the fifth calculation unit in each of the plurality of sections. The sixth calculation unit that calculates the second predicted value of the third index that indicates the degree of change in the orbital displacement after the orbital displacement is measured by the second calculation unit based on the fourth calculated value of the 1 correction coefficient. And have.

Further, as another aspect, the fifth calculation unit calculates the first predicted value by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections, and the calculated first. The first correction coefficient, which is the ratio of the third calculated value to the one predicted value, may be calculated.

Further, as another aspect, the sixth calculation unit calculates the third predicted value of the second index by substituting the second calculated value as the first index into the regression equation in each of the plurality of sections. The second predicted value may be calculated by multiplying the calculated third predicted value by the first correction coefficient.

Further, as another aspect, the orbital displacement prediction system measures the orbital displacement again at a plurality of measurement positions in each of the plurality of sections after the orbital displacement is measured by the second calculation unit, and the first index. Is calculated again by the 7th calculation unit, and the 7th calculation unit is based on the 2nd calculation value and the 5th calculation value of the 1st index calculated by the 7th calculation unit in each of the plurality of sections. It may have an eighth calculation unit for calculating a fourth index indicating the degree of change in the orbital displacement before the orbital displacement is measured. Further, the orbital displacement prediction system shows the relationship between the third predicted value, the sixth calculated value of the fourth index calculated by the eighth calculation unit, and the first correction coefficient in each of the plurality of sections. The ninth calculation unit for calculating the second correction coefficient, the fifth calculation value, the regression equation, the fourth calculation value, and the second correction coefficient calculated by the ninth calculation unit in each of the plurality of sections. It has 7 calculated values and a 10th calculation unit that calculates the 4th predicted value of the 5th index indicating the degree of change in the orbital displacement after the orbital displacement is measured by the 7th calculation unit. You may.

Further, as another aspect, the ninth calculation unit calculates the second correction coefficient, which is the ratio of the sixth calculated value to the product of the third predicted value and the first correction coefficient, in each of the plurality of sections. You may.

Further, as another aspect, the fifth calculation unit calculates the first predicted value by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections, and the calculated first. The first correction coefficient, which is the difference between the first predicted value and the third calculated value, may be calculated.

By applying one aspect of the present invention, in the orbital displacement prediction method for predicting orbital displacement, future orbital displacement can be predicted with high accuracy even when the historical data of orbital displacement is small and insufficient.

It is a block diagram which shows the structure of the orbital displacement prediction system of Embodiment 1. FIG. It is a flow chart which shows some steps of the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the first measurement of the orbital displacement by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the second measurement of the orbital displacement by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the calculation of the regression equation by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the calculation of the correction coefficient by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the third measurement of the orbital displacement by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the calculation of the correction coefficient by the orbital displacement prediction method of Embodiment 1. FIG. It is a figure for demonstrating the calculation of the correction coefficient by the orbital displacement prediction method of the modification of Embodiment 1. FIG. It is a figure for demonstrating the calculation of the regression equation by the orbital displacement prediction method of Embodiment 2. It is a figure for demonstrating the calculation of the correction coefficient by the orbital displacement prediction method of Embodiment 2. It is a figure for demonstrating the calculation of the correction coefficient by the orbital displacement prediction method of Embodiment 2.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

It should be noted that the disclosure is merely an example, and those skilled in the art can easily conceive of appropriate changes while maintaining the gist of the invention are naturally included in the scope of the present invention. Further, in order to clarify the description, the drawings may schematically represent the width, thickness, shape, etc. of each part as compared with the embodiment, but this is just an example, and the interpretation of the present invention is used. It is not limited.

Further, in the present specification and each of the drawings, the same elements as those described above with respect to the above-described drawings may be designated by the same reference numerals, and detailed description thereof may be omitted as appropriate.

Further, in the drawings used in the embodiment, hatching (shading) may be omitted in order to make the drawings easier to see even if they are cross-sectional views. Further, even if it is a plan view, hatching may be added to make the drawing easier to see.

In the following embodiments, when the range is indicated as A to B, A or more and B or less are indicated unless otherwise specified.

(Embodiment 1)
<Orbital displacement prediction system and orbital displacement prediction method>
First, the track displacement prediction system and the track displacement prediction method of the first embodiment will be described. The orbital displacement prediction system of the first embodiment is an orbital displacement prediction system that predicts the orbital displacement in each of a plurality of sections in an orbit including a plurality of sections arranged along the length direction of the orbit. The orbital displacement prediction method of the first embodiment is an orbital displacement prediction method for predicting the orbital displacement in each of a plurality of sections in an orbit including a plurality of sections arranged along the length direction of the orbit. This is an orbital displacement prediction method using the orbital displacement prediction system of Form 1.

FIG. 1 is a block diagram showing a configuration of the orbital displacement prediction system of the first embodiment. FIG. 2 is a flow chart showing some steps of the orbital displacement prediction method of the first embodiment. FIG. 3 is a diagram for explaining the first measurement of the orbital displacement by the orbital displacement prediction method of the first embodiment. FIG. 4 is a diagram for explaining the second measurement of the orbital displacement by the orbital displacement prediction method of the first embodiment. FIG. 5 is a diagram for explaining the calculation of the regression equation by the orbital displacement prediction method of the first embodiment. FIG. 6 is a diagram for explaining the calculation of the correction coefficient by the orbital displacement prediction method of the first embodiment.

As shown in FIG. 1, the orbital displacement prediction system 10 of the first embodiment has a first calculation unit 11, a second calculation unit 12, a third calculation unit 13, a fourth calculation unit 14, and a fifth. It has a calculation unit 15, a sixth calculation unit 16, a seventh calculation unit 17, an eighth calculation unit 18, a ninth calculation unit 19, and a tenth calculation unit 20. The calculation unit 21 is composed of the first calculation unit 11 to the tenth calculation unit 20. Further, the track displacement prediction system of the first embodiment may include a measurement unit 22 for measuring the track displacement, and a control unit 23 for controlling the operation of the calculation unit 21 and the measurement unit 22. As the first calculation unit 11 to the tenth calculation unit 20, that is, the calculation unit 21, and the control unit 23, for example, a computer that executes a program for causing each calculation unit to perform a constant operation can be used.

The measuring unit 22 is provided in, for example, a track inspection vehicle, and measures the track displacement, which is the displacement of the track, when the track inspection vehicle travels on the track. Further, as described above, the track displacement is based on the high-low displacement, which is the vertical displacement of the rail, the street displacement, which is the displacement in the width direction (left-right direction) of the rail, and the set value of the distance between the rails on both the left and right sides. The gap displacement, which is the difference between the two rails, the level displacement, which is the difference from the set value of the height difference between the left and right rails, and the flat displacement, which is the level difference between two points separated by a certain distance. It can be exemplified. As the measuring unit 22, various measuring devices capable of appropriately measuring the various orbital displacements illustrated can be used.

In the orbital displacement prediction method of the first embodiment, first, the first calculation unit 11 (see FIG. 1) has a plurality of sections SC arranged along the length direction of the orbital RA as shown in FIG. In each of the plurality of sections SC in the including orbit RA, the orbital displacement TR is measured by the measuring unit 22 (see FIG. 1) at a plurality of measurement position MPs different from each other along the length direction of the orbit RA, and the plurality of measurement position MPs are measured. The index IN1 representing the variation of the measured values of the plurality of orbital displacement TRs measured in each of the above is calculated (step S11 in FIG. 2).

Preferably, the standard deviation or the maximum value of the measured values of the plurality of orbital displacement TRs can be used as the index IN1, but the case where the standard deviation is used will be illustrated below. In such a case, as shown in FIG. 2, in step S11, the standard deviation of the first orbital displacement TR is calculated. In the specification of the present application, the first orbital displacement TR means the orbital displacement TR of the first measurement, and the same applies to the second and subsequent times.

FIG. 3 shows the measured values obtained by performing the first measurement of the orbital displacement TR in step S11. In FIG. 3, as an example, the five section SCs are displayed as section SC1, section SC2, section SC3, section SC4, and section SC5. Further, in FIG. 3, the first track displacement TR is represented by a solid line as the track displacement TR1.

When the standard deviation of the measured values of the plurality of orbital displacement TRs is used as the index IN1, as shown in FIG. 3, the calculated value CV1 of the index IN1 is set at each of the plurality of measurement position MPs in each of the plurality of sections SC. A calculated value of the standard deviation σ ₁ of the measured values of the plurality of measured orbital displacements TR can be used. Then, the calculated value CV1 of the index IN1 can be regarded as the standard deviation of the first orbital displacement TR and can be regarded as the first orbital displacement TR.

In the following, the standard deviation of the orbital displacement TR generalized without specifying how many times the orbital displacement TR is measured is defined as the standard deviation σ.

In the orbital displacement prediction method of the first embodiment, after the first calculation unit 11 measures the orbital displacement TR by the measurement unit 22 in step S11, the second calculation unit 12 (see FIG. 1) is shown in FIG. As described above, in each of the plurality of section SCs, the orbital displacement TR is measured again by the measuring unit 22 at the plurality of measurement position MPs, and the index IN1 is calculated again (step S12 in FIG. 2).

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S12, the standard deviations of the second orbital displacement TRs are calculated as shown in FIG. .. Further, after the first measurement of the orbital displacement TR and the elapse of a predetermined period, the second measurement of the orbital displacement TR is performed, but usually, after the first measurement of the orbital displacement TR, the measurement is performed. For example, after a period of several months to one year, the second orbital displacement TR can be measured.

In FIG. 4, as in FIG. 3, as an example, the five section SCs are displayed as section SC1, section SC2, section SC3, section SC4, and section SC5. Further, in FIG. 4, for easy understanding, the second orbital displacement TR is indicated by a solid line as the orbital displacement TR2, and the orbital displacement TR of the first measurement is indicated by a broken line as the orbital displacement TR1.

As described above, when the standard deviation of the measured values of the plurality of orbital displacement TRs is used as the index IN1, as shown in FIG. 4, the calculated value CV2 of the index IN1 is used as the calculated value CV2 of the plurality of section SCs. A calculated value of the standard deviation σ ₂ of the measured values of the plurality of orbital displacements TR measured in each of the MPs can be used. Then, the calculated value CV2 of the index IN1 can be regarded as the standard deviation of the second orbital displacement TR and can be regarded as the second orbital displacement TR.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 4, the third calculation unit 13 (see FIG. 1) is the first calculation unit in step S11 in each of the plurality of section SCs. Based on the calculated value CV1 of the index IN1 calculated by 11 and the calculated value CV2 of the index IN1 calculated by the second calculation unit 12 in step S12, the first calculation unit 11 is the measurement unit in step S11. An index IN2 indicating the degree of change in the orbital displacement TR after the orbital displacement TR is measured by 22 and before the second calculation unit 12 measures the orbital displacement TR by the measurement unit 22 is calculated in step S12 ( Step S13 in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S13, the differences between the first and second standard deviations are calculated, as shown in FIG. .. Further, as the calculated value CV3 of the index IN2, the calculated value of the difference Δσ ₁₂ of the first and second standard deviations can be used. That is, as the index IN2, the difference between the calculated value CV1 of the index IN1 and the calculated value CV2 of the index IN1 can be used. Further, the difference Δσ ₁₂ of the first and second standard deviations is calculated by the following equation (Equation 1).

In the following, the difference in standard deviation between two consecutive measurements of orbital displacement TR, which is generalized without specifying how many times the orbital displacement TR is measured, is defined as the difference in standard deviation Δσ.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 5, the fourth calculation unit 14 (see FIG. 1) is subjected to each of the plurality of section SCs by the first calculation unit 11 in step S11. The calculated value CV1 (standard deviation σ ₁ ) of the plurality of indexes IN1 calculated in each of the above, and the calculated value CV3 of the plurality of indexes IN2 calculated in each of the plurality of sections SC by the second calculation unit 12 in step S12. Based on (difference Δσ _{12 of the} standard deviation), a regression equation RE1 showing the relationship between the index IN1 and the index IN2 is calculated (step S14 in FIG. 2). In addition, FIG. 5 schematically shows a graph in which the horizontal axis is the standard deviation σ of the orbital displacement TR and the vertical axis is the difference Δσ of the standard deviation.

As described above, when the standard deviations of the measured values of a plurality of orbital displacement TRs are used as the index IN1, in step S14, the regression equation is derived from the standard deviation σ ₁ and the difference Δσ _{12 of the} standard deviations, as shown in FIG. RE1 will be calculated.

As shown in FIG. 5, the horizontal axis is the standard deviation σ of the orbital displacement TR, and the vertical axis is the difference Δσ of the standard deviation. The calculated value CV1 of the index IN1 calculated for each of the plurality of sections SC (CV1 Plot the set data of the standard deviation σ ₁ ) and the calculated value CV3 (standard deviation difference Δσ ₁₂ ) of the index IN2. Then, a regression calculation is performed using the regression equation RE1 represented by the following equation (Equation 2) or the following equation (Equation 3) as an example of the following equation (Equation 2) so that the correlation coefficient becomes maximum, for example. The values of a and b are determined. By such a method, the regression equation RE1 can be calculated.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 6, the fifth calculation unit 15 (see FIG. 1) is the first calculation unit in step S11 in each of the plurality of section SCs. The predicted value PV1 of the index IN2 is calculated based on the calculated value CV1 (standard deviation σ ₁ ) of the index IN1 calculated by 11 and the regression equation RE1, and the predicted value PV1 of the calculated index IN2 and the index The correction coefficient CF1 indicating the relationship with the calculated value CV3 of IN2 is calculated (step S15 in FIG. 2). Note that FIG. 6 schematically shows a graph in which the horizontal axis is the standard deviation σ of the orbital displacement TR and the vertical axis is the difference Δσ of the standard deviation, as in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S15, the fifth calculation unit 15 corrects the difference Δσ ₁₂ of the standard deviations, as shown in FIG. The coefficient CF1 will be calculated.

Preferably, as shown in FIG. 6, the fifth calculation unit 15 predicts the index IN2 by substituting the calculated value CV1 as the index IN1 into the regression equation RE1 in each of the plurality of sections SC in step S15. The value PV1 is calculated. In addition, preferably, as shown in FIG. 6, in step S15, in step S15, the ratio of the calculated value CV3 of the index IN2 to the predicted value PV1 of the calculated index IN2 in each of the plurality of section SCs. The correction coefficient CF1 is calculated. Further, assuming that the correction coefficient CF ₁ is expressed as the correction coefficient γ ₁ , the correction coefficient γ ₁ is expressed by the following equation (Equation 4).

Here, the molecule on the right side of the equation of the above equation (Equation 4) represents the calculated value CV3 (difference Δσ _{12 of the} standard deviation) of the index IN2, and the denominator on the right side of the equation of the above equation (Equation 4) is It represents the predicted value PV1 of the index IN2.

When the regression equation RE1 is expressed by the above equation (Equation 3), the calculated value CV3 (standard deviation difference Δσ ₁₂ ) of the index IN2 satisfies the correction equation CE1 expressed by the following equation (Equation 5). become. In FIG. 6, the regression equation RE1 is indicated by a solid line, and the correction equation CE1 is indicated by a broken line.

In the first embodiment, in step S15, the correction coefficient is calculated from the predicted value of the orbital displacement by the basic model (regression equation) and the measured value of the actual orbital displacement. As shown in FIG. 6, in the first embodiment, as an example of the calculation method, a method of calculating the correction coefficient by dividing the measured value of the actual track displacement by the predicted value of the track displacement by the basic model is used. Shown. By such a method, the correction coefficient can be easily calculated.

That is, in the first embodiment, in steps S11 to S15, a basic model for predicting the track displacement is constructed in a somewhat long section, and a correction coefficient is applied to the track displacement predicted by the basic model for each short section. Multiply by γ ₁ . The basic model calculates, for example, the advance of the standard deviation of the orbital displacement from the standard deviation of the initial orbital displacement or the wheel load. As shown in FIGS. 3 and 4, the initial orbital displacement and the advance of the orbital displacement, which are input values, are calculated from the measured values of the orbital displacement, and as shown in FIG. 5, regression analysis is performed from the plot of the measured values of the orbital displacement. Estimate the approximate curve by etc. and build the basic model.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 6, the sixth calculation unit 16 (see FIG. 1) is the second calculation unit in step S12 in each of the plurality of section SCs. Based on the calculated value CV2 of the index IN1 calculated in step 12, the regression equation RE1, and the calculated value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15, the second step in step S12. The calculation unit 12 calculates the predicted value PV2 of the index IN3 indicating the degree of change in the orbital displacement TR after the orbital displacement TR is measured by the measuring unit 22 (step S16 in FIG. 2).

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S16, the sixth calculation unit 16 determines the standard deviations of the second and third times, as shown in FIG. The difference will be predicted. Further, assuming that the predicted value PV2 of the index IN3 is expressed as the predicted value Δσ ₂ ^* of the difference between the second and third standard deviations, the predicted value PV2 of the index IN3 is expressed by the following equation (Equation 6).

Here, assuming that the factor on the left side of the right side of the equation (Equation 6) is the predicted value PV3 of the index IN2, the predicted value PV3 of the index IN2 is the calculated value CV2 (standard) as the index IN1 in the regression equation RE1. It is calculated by substituting the deviation σ ₂ ). That is, preferably, in step S16, the sixth calculation unit 16 calculates the predicted value PV3 of the index IN2 by substituting the calculated value CV2 as the index IN1 into the regression equation RE1 in each of the plurality of sections SC. , The predicted value PV2 of the index IN3 is calculated by multiplying the calculated predicted value PV3 of the index IN2 by the correction coefficient CF1. By such a method, the predicted value PV2 of the index IN3 can be easily calculated.

In the conventional method of predicting orbital displacement, when the historical data of orbital displacement acquired in the past is sufficiently accumulated, the orbital displacement is predicted based on the accumulated data. However, if the track displacement history data is not sufficiently accumulated, or if the track structure, vehicle, driving, etc. conditions change even if the track displacement history data is sufficiently accumulated, the accuracy is high. It was difficult to predict the orbital displacement.

Further, in the conventional method for creating a track maintenance plan, acceleration or vehicle sway is predicted by simulation and used in the track maintenance plan. At this time, it was necessary to correct the track displacement (the amount of unevenness on the road surface) by comparing the design value with the measured value.

On the other hand, in the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, the calculated value CV1 of the index IN1 indicating the variation of the orbital displacement TR measured the first time and the orbital displacement measured the second time. Based on the calculated value CV2 of the index IN1 representing the variation of TR, the index IN2 indicating the degree of change in the orbital displacement TR before the second measurement is calculated, and a regression equation showing the relationship between the index IN1 and the index IN2 is shown. Calculate RE1. Further, in the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, a correction showing the relationship between the predicted value PV1 of the index IN2 calculated based on the regression equation RE1 and the calculated value CV3 of the index IN2. Based on the calculated value CV4 of the coefficient CF1, the index IN3 indicating the degree of change in the orbital displacement TR after the second measurement is predicted.

Even if the history data of the orbital displacement is small, it is possible to confirm the tendency of the change of the orbital displacement within the section if the measurement data for several times is obtained for the orbital displacement in a long section. is there. Therefore, in the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, a basic model (regression equation) for predicting the tendency of the orbital displacement change within a somewhat long section is first constructed, and then the section. Roughly predict changes in internal orbital displacement. Next, the calculation result is corrected by the basic model by dividing into shorter sections and setting different correction coefficients for each shorter section. The basic model calculates, for example, the advance of the standard deviation of the orbital displacement from the standard deviation of the initial orbital displacement or the wheel load.

Therefore, in the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, it is sufficient if there is a measured value of the orbital displacement measured in the past two measurements, and it is necessary to perform a larger number of measurements. Absent. Therefore, even if the historical data of the orbital displacement is small and insufficient, the future orbital displacement can be predicted with high accuracy. Further, even if the track displacement history data is sufficiently accumulated, it is difficult to predict the track displacement with high accuracy when the conditions such as the track structure, the vehicle, or the driving are changed. According to the first embodiment, even in such a case, the future orbital displacement can be predicted with high accuracy. In the first embodiment, the advance of the standard deviation of the orbital displacement is calculated from the standard deviation of the initial orbital displacement, but in the second embodiment, the advance of the standard deviation of the orbital displacement is calculated from the initial wheel load. ..

Further, in the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, a model for predicting the future orbital displacement from the measurement result of the orbital displacement is created, and the measured values of the orbital displacements for the past two times are used. By comparing with the predicted value of the orbital displacement for one time by the created model, the predicted value of the orbital displacement after that is further corrected. Therefore, future orbital displacement can be predicted with high accuracy without performing simulation.

Further, according to the orbital displacement prediction method using the orbital displacement prediction system of the first embodiment, the life cycle cost is calculated by calculating the predicted value of the orbital maintenance cycle from the calculated orbital displacement predicted value. It is also possible to do.

Further, in the track displacement prediction method using the track displacement prediction system of the first embodiment, the correction coefficient can be set according to the characteristics of each short section or the tendency of the change of the track displacement.

Further, in the track displacement prediction method using the track displacement prediction system of the first embodiment, the correction coefficient can be updated every time the measurement data of the track displacement is added. The update of the correction coefficient will be described below.

FIG. 7 is a diagram for explaining the third measurement of the orbital displacement by the orbital displacement prediction method of the first embodiment. FIG. 8 is a diagram for explaining the calculation of the correction coefficient by the orbital displacement prediction method of the first embodiment.

Preferably, after the second calculation unit 12 measures the orbital displacement TR by the measurement unit 22 in step S12, the seventh calculation unit 17 (see FIG. 1) of the plurality of sections SC, as shown in FIG. In each case, the orbital displacement TR is measured again by the measuring unit 22 at a plurality of measurement position MPs, and the index IN1 is calculated again (step S17 in FIG. 2).

When the standard deviation of the measured values of the plurality of orbital displacement TRs is used as the index IN1, the standard deviation of the third orbital displacement TR is calculated in step S17 as shown in FIG. Further, after the second measurement of the orbital displacement TR and the elapse of a predetermined period, the third measurement of the orbital displacement TR is performed. For example, after the first measurement of the orbital displacement TR, 2 After a period equal to the period until the third orbital displacement TR measurement is performed, the third orbital displacement TR measurement can be performed.

In FIG. 7, as in FIG. 3, as an example, the five section SCs are displayed as section SC1, section SC2, section SC3, section SC4, and section SC5. Further, in FIG. 7, for easy understanding, the third orbital displacement TR is indicated by a solid line as the orbital displacement TR3, and the second orbital displacement TR is indicated by a broken line as the orbital displacement TR2.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, as shown in FIG. 7, the calculated value CV5 of the index IN1 is used as a plurality of measurement positions in each of the plurality of sections SC. A calculated value of the standard deviation σ ₃ of the measured values of the plurality of orbital displacement TRs measured in each of the MPs can be used. Then, the calculated value CV5 of the index IN1 can be regarded as the standard deviation of the third orbital displacement TR and can be regarded as the third orbital displacement TR.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 7, the eighth calculation unit 18 (see FIG. 1) is the second calculation unit in step S12 in each of the plurality of section SCs. Based on the calculated value CV2 of the index IN1 calculated in step 12 and the calculated value CV5 of the index IN1 calculated by the seventh calculation unit 17 in step S17, the second calculation unit 12 is the measurement unit in step S12. An index IN4 indicating the degree of change in the orbital displacement TR after the orbital displacement TR is measured by 22 and before the seventh calculation unit 17 measures the orbital displacement TR by the measurement unit 22 in step S17 is calculated ( Step S18 in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S18, the differences of the second and third standard deviations are calculated as shown in FIG. .. Further, as the calculated value CV6 of the index IN4, the calculated value of the difference Δσ ₂₃ of the second and third standard deviations can be used. Further, the difference Δσ ₂₃ of the second and third standard deviations is calculated by the following equation (Equation 7).

In the orbital displacement prediction method of the first embodiment, next, the ninth calculation unit 19 (see FIG. 1) sets the predicted value PV3 of the index IN2 and the predicted value PV3 of the index IN2 in each of the plurality of section SCs as shown in FIG. In step S18, the correction coefficient CF2 indicating the relationship between the calculated value CV6 of the index IN4 calculated by the eighth calculation unit 18 and the correction coefficient CF1 is calculated (step S19 in FIG. 2). Note that FIG. 8 schematically shows a graph in which the horizontal axis is the standard deviation σ of the orbital displacement TR and the vertical axis is the difference Δσ of the standard deviation, as in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S19, the ninth calculation unit 19 corrects the difference Δσ ₂₃ of the standard deviations, as shown in FIG. The coefficient CF2 will be calculated.

Preferably, as shown in FIG. 8, in step S19, the ninth calculation unit 19 calculates the index IN4 with respect to the product of the predicted value PV3 of the index IN2 and the correction coefficient CF1 in each of the plurality of sections SC. The correction coefficient CF2, which is the ratio of CV6, is calculated. Further, assuming that the correction coefficient CF ₂ is expressed as the correction coefficient γ ₂ , the correction coefficient γ ₂ is expressed by the following equation (Equation 8).

Here, the molecule on the right side of the equation of the above equation (Equation 8) represents the calculated value CV6 (difference Δσ _{23 of the} standard deviation) of the index IN2, and is among the denominators on the right side of the equation of the above equation (Equation 8). The factor on the left side represents the predicted value PV3 of the index IN2, and is calculated by substituting the calculated value CV2 (standard deviation σ ₂ ) as the index IN1 into the regression equation RE1.

When the regression equation RE1 is expressed by the above equation (Equation 3), the calculated value CV6 (standard deviation difference Δσ ₂₃ ) of the index IN4 satisfies the correction equation CE2 expressed by the following equation (Equation 9). become. In FIG. 8, the regression equation RE1 is indicated by a solid line, and the correction equation CE1 and the correction equation CE2 are indicated by a broken line.

In such a case, in step S18, the correction coefficient can be updated every time the measurement data of the orbital displacement is added.

In the orbital displacement prediction method of the first embodiment, next, as shown in FIG. 8, the tenth calculation unit 20 (see FIG. 1) is the seventh calculation unit in step S17 in each of the plurality of section SCs. The calculated value CV5 of the index IN1 calculated in step 17, the regression equation RE1, the calculated value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15, and the ninth calculation unit 19 in step S19. Based on the calculated correction coefficient CF2 calculated value CV7, the index IN5 indicating the degree of change in the orbital displacement TR after the seventh calculation unit 17 measures the orbital displacement TR by the measurement unit 22 in step S17. The predicted value PV4 is calculated (step S20 in FIG. 2).

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S20, the tenth calculation unit 20 determines the standard deviations of the third and fourth times, as shown in FIG. The difference will be predicted. Further, assuming that the predicted value PV4 of the index IN5 is expressed as the predicted value Δσ ₃ ^* of the difference between the third and fourth standard deviations, the predicted value PV4 of the index IN5 is expressed by the following equation (Equation 10).

Here, the leftmost factor of the right-hand side of the equation (Equation 10) is calculated by substituting the calculated value CV5 (standard deviation σ ₃ ) as the index IN1 into the regression equation RE1.

By performing steps S17 to S20, each time the track displacement data is additionally obtained, the predicted value and the measured value of the track displacement are additionally obtained, so that the correction coefficient is updated. By repeatedly acquiring orbital displacement data and updating the correction coefficient, it becomes possible to predict orbital displacement with higher accuracy.

In addition, step S17 to step S20 can be repeated. That is, the measurement of the orbital displacement can be repeated as the fourth time, the fifth time, and the i-th time (i is a natural number of 2 or more) as in the third time. Then, after the measurement of the i-th orbit displacement, the i-th, in the case of predicting the difference between (i + 1) th standard deviation is, the i-th, i + 1 th of the predicted value of the difference between the standard deviation Δσ _i ^* is represented by the following It is represented by the equation (Equation 11).

Here, the factor on the left side of the right side of the equation of the above equation (Equation 11) is the orbit after the i-th orbital displacement TR is measured and before the i + 1th orbital displacement TR is measured. It represents a predicted value of an index showing the degree of change in the displacement TR. Further, the factor on the right side of the right side of the equation of the above equation (Equation 11) represents a correction coefficient, and is represented by the following equation (Equation 12).

In this way, the measurement of the orbital displacement can be repeated for the fourth and fifth times, the correction coefficient can be updated as in the third time, and the predicted value can be corrected as in the third time. ..

By repeating steps S17 to S20, the acquisition of the orbital displacement data and the update of the correction coefficient are repeated, and the orbital displacement can be predicted with higher accuracy. Further, by tracking the change of the correction coefficient, it is possible to extract the section in which the correction coefficient is rapidly increasing as the section in which the orbital displacement is rapidly advancing.

Further, in the track displacement prediction method using the track displacement prediction system of the first embodiment, when the conditions such as the track structure, the vehicle, or the driving change, for example, the regression equation RE1 is recalculated to obtain a basic model. Is changed according to the change of conditions, and the correction coefficient is applied as it is. Then, by predicting the influence and effect of future track displacement on the transition of track displacement in response to changes in conditions, it is possible to study measures such as improving track structure, updating vehicles, and improving speed. Is. In addition, since future changes in orbital displacement can be calculated even when conditions change, measures can be evaluated by comparing changes in life cycle costs with and without measures. Therefore, it is possible to realize a track displacement prediction method and a track displacement prediction system that predict future track displacements that can respond to changes in conditions such as track structure, vehicle, or driving.

<Modification example of track displacement prediction system and track displacement prediction method>
Next, a modified example of the track displacement prediction system and the track displacement prediction method of the first embodiment will be described. In the orbital displacement prediction method of this modification, the correction coefficient CF1 is the ratio of the calculated value CV3 of the index IN2 to the calculated predicted value PV1 of the index IN2, instead of the calculated value PV1 of the index IN2. It differs from the orbital displacement prediction method of the first embodiment in that it is a difference of the calculated value CV3 of the index IN2.

FIG. 9 is a diagram for explaining the calculation of the correction coefficient by the orbital displacement prediction method of the modified example of the first embodiment. Note that FIG. 9 schematically shows a graph in which the horizontal axis is the standard deviation σ of the orbital displacement TR and the vertical axis is the difference Δσ of the standard deviation, as in FIG.

In the orbital displacement prediction method using the orbital displacement prediction system of this modification, after performing steps S11 to S14 in the same manner as in the first embodiment, in step S15, the fifth calculation unit 15 is shown in FIG. In addition, the predicted value PV1 of the index IN2 is calculated based on the calculated value CV1 (standard deviation σ ₁ ) of the index IN1 and the regression equation RE1 in each of the plurality of sections SC, and the calculated prediction of the index IN2 is performed. The correction coefficient CF1 indicating the relationship between the value PV1 and the calculated value CV3 of the index IN2 is calculated. Preferably, in step S15, the fifth calculation unit 15 calculates the predicted value PV1 of the index IN2 by substituting the calculated value CV1 as the index IN1 into the regression equation RE1 in each of the plurality of section SCs.

However, in the present modification, in step S15, unlike the first embodiment, the fifth calculation unit 15 is the difference between the calculated predicted value PV1 of the index IN2 and the calculated value CV3 of the index IN2 as shown in FIG. The correction coefficient CF1 is calculated. Additionally, if you represent a correction factor CF1 as the correction coefficient gamma _1, the correction coefficient gamma ₁ is expressed by the following equation (Equation 13).

Here, the term on the left side of the right side of the equation of the above equation (Equation 13) represents the calculated value CV3 (standard deviation difference Δσ ₁₂ ) of the index IN2, and is the right side of the equation of the above equation (Equation 13). The term on the right side represents the predicted value PV1 of the index IN2.

When the regression equation RE1 is expressed by the above equation (Equation 3), the calculated value CV3 (standard deviation difference Δσ ₁₂ ) of the index IN2 satisfies the correction equation CE3 expressed by the following equation (Equation 14). become. In FIG. 9, the regression equation RE1 is indicated by a solid line, and the correction equation CE3 is indicated by a broken line.

In this modification as well, as in the first embodiment, in step S15, the correction coefficient is calculated from the predicted value of the track displacement by the basic model and the measured value of the actual track displacement. However, as shown in FIG. 9, in this modification, as an example of the calculation method, unlike the first embodiment, the actual measured value of the orbital displacement is used as the predicted value of the orbital displacement by the basic model. The method of calculating by the difference between the measured value of the actual orbital displacement and the actual measured value is shown.

In the orbital displacement prediction method using the orbital displacement prediction system of the present modification, in step S16, as in the first embodiment, the sixth calculation unit 16 is performed in each of the plurality of sections SC as shown in FIG. , The calculated value CV2 of the index IN1 calculated by the second calculation unit 12 in step S12, the regression equation RE1, and the calculated value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15. Based on this, the second calculation unit 12 calculates the predicted value PV2 of the index IN3 indicating the degree of change in the orbital displacement TR after the orbital displacement TR is measured by the measurement unit 22 in step S12.

In this modified example as well, in step S16, the fifth calculation unit 15 predicts the difference between the standard deviations of the second and third times, as in the first embodiment. However, if the predicted value PV2 of the index IN3 is expressed as the predicted value Δσ ₂ ^* of the difference between the second and third standard deviations, in this modification, in step S16, unlike the first embodiment, the index IN3 The predicted value PV2 is represented by the following equation (Equation 15).

Here, the term on the left side of the right side of the equation (Equation 15) is calculated by substituting the calculated value CV2 (standard deviation σ ₂ ) as the index IN1 into the regression equation RE1.

In the orbital displacement prediction method of this modification, the correction coefficient CF1 is the ratio of the calculated value CV3 of the index IN2 to the calculated predicted value PV1 of the index IN2, instead of the calculated value PV1 of the index IN2. The same can be applied to the first embodiment except that the difference is the calculated value CV3 of the index IN2. Therefore, even in the orbital displacement prediction method using the orbital displacement prediction system of this modification, for example, even if the historical data of the orbital displacement is small and insufficient, the future orbital displacement can be predicted with high accuracy. It has the same effect as the orbital displacement prediction method using the orbital displacement prediction system of.

(Embodiment 2)
<Orbital displacement prediction system and orbital displacement prediction method>
Next, the track displacement prediction system and the track displacement prediction method of the second embodiment will be described. The orbital displacement prediction method of the second embodiment replaces the regression equation RE1 which shows the relationship between the index IN1 which shows the variation of the measured values of the plurality of orbital displacement TRs and the index IN2 which shows the degree of change of the orbital displacement TRs. The method for predicting the orbital displacement according to the first embodiment is to use the regression equation RE2 which indicates the relationship between the index indicating the wheel load in each of the plurality of sections SC and the index IN2 indicating the degree of change in the orbital displacement. Different from.

FIG. 10 is a diagram for explaining the calculation of the regression equation by the orbital displacement prediction method of the second embodiment. 11 and 12 are diagrams for explaining the calculation of the correction coefficient by the orbital displacement prediction method of the second embodiment.

In the orbital displacement prediction method using the orbital displacement prediction system of the second embodiment, in step S11, as in the first embodiment, the first calculation unit 11 (see FIG. 1) is as shown in FIG. , In each of the plurality of sections SC, the orbital displacement TR is measured at a plurality of measurement position MPs different from each other along the length direction of the orbit RA, and a plurality of orbital displacement TRs measured at each of the plurality of measurement position MPs. Based on the measured values of, the index IN1 representing the variation of the measured values of the plurality of orbital displacement TRs is calculated. Preferably, the standard deviation or the maximum value of the measured values of the plurality of orbital displacement TRs can be used as the index IN1, but the case where the standard deviation is used will be illustrated below.

On the other hand, in the second embodiment, in step S11, unlike the first embodiment, the first calculation unit 11 is based on the measured values of the plurality of orbital displacement TRs measured at each of the plurality of measurement position MPs. , In addition to the index IN1, the cumulative wheel load WL1 in each of the plurality of section SCs is calculated as an index representing the wheel load in each of the plurality of section SCs.

Here, when the cumulative wheel weight is used as an index representing the wheel weight, the wheel weight per wheel acting on the track is calculated according to the following formula (Equation 16) to the following formula (Equation 21) and passes on the track. Calculate the cumulative wheel weight by multiplying the number of wheels.

First, when the cumulative wheel load WL1 is expressed as the cumulative wheel load P, the cumulative wheel load P has a wheel load P _st due to the load of the vehicle, an inertial force ΔP _sp due to high and low displacements, and a dynamic wheel load ΔP _{un sp due} to rail unevenness. It is expressed by the following equation (Equation 16).

Here, the inertial force [Delta] P _sp by height displacement, and the dynamic wheel load [Delta] P _Unsp by rail irregularities, to the wheel load _{P st} by the load of the vehicle, representing the wheel load by orbital state.

Further, the straight section, the inner of the curved section rail side, and the wheel load P _st is due to the load of the vehicle for the curve outside in the curve section, the following equation (Equation 17), the following equation (Equation 18), and the following formula It is represented by (Equation 19).

Further, the inertial force ΔP _sp due to the high and low displacement and the dynamic wheel load ΔP _unsp due to the unevenness of the rail are expressed by the following equations (Equation 20) and the following equation (Equation 21).

The variables in the above equation (Equation 17) to the above equation (Equation 21) are the variables shown below.
W ₀ : Axial load (kN) when the vehicle is stationary
H _G ^*: effective height of the center of gravity of the vehicle (m)
v: Vehicle running speed (m / s)
V: Vehicle running speed (km / h)
R: Curve radius (m)
C: Kant (m)
G: Gauge (m)
z: High and low displacement (mm)
α: Coefficient depending on the state of the seam

As shown in the above equation (Equation 16), the cumulative wheel load WL1 (cumulative wheel load P) depends on the inertial force ΔP _sp due to the high and low displacements, and as shown in the above equation (Equation 20), the inertial force due to the high and low displacements. ΔP _sp depends on the high-low displacement z, and the high-low displacement z depends on the index IN1 (standard deviation σ ₁ ). Therefore, when the cumulative wheel load _{P 1} of the cumulative wheel load WL1 (cumulative wheel load P) obtained in step S11 in the first calculation unit 11 measures the orbital displacement TR by measuring unit 22, the cumulative wheel load WL1 (cumulative wheel load _{P 1)} is dependent on the calculated value CV1 of the index IN1 (standard deviation sigma _1).

In the second embodiment, after the first calculation unit 11 measures the track displacement TR by the measurement unit 22 in step S11, in step S12, the second calculation unit 12 (see FIG. 1) is the same as the first embodiment. Similarly, as shown in FIG. 4, the orbital displacement TR is measured again by the measuring unit 22 at a plurality of measuring position MPs in each of the plurality of section SCs, and the index IN1 is calculated again.

On the other hand, in the second embodiment, in step S12, unlike the first embodiment, the second calculation unit 12 has, in addition to the index IN1, a plurality of indexes representing the wheel load in each of the plurality of section SCs. The cumulative wheel load WL1 in each section SC is calculated again. The calculation of the cumulative wheel load WL1 in step S12 can be the same as the calculation of the cumulative wheel load WL1 in step S11. Therefore, the cumulative wheel load WL1 to the second calculation unit 12 is obtained by measuring the track displacement TR by measuring unit 22 at step S12 (the cumulative wheel load P) and cumulative wheel load _{P 2,} the accumulated wheel load WL1 (cumulative wheel load _{P 2)} is dependent on the calculated value CV2 of the index IN1 (standard deviation sigma _2).

In the second embodiment, then, in step S13, similarly to the first embodiment, the third calculation unit 13 (see FIG. 1) is the index IN1 calculated by the first calculation unit 11 in step S11. Based on the calculated value CV1 and the calculated value CV2 of the index IN1 calculated by the second calculation unit 12 in step S12, the first calculation unit 11 measured the trajectory displacement TR by the measurement unit 22 in step S11. After that, and in step S12, the second calculation unit 12 calculates the index IN2 indicating the degree of change in the track displacement TR before the measurement unit 22 measures the track displacement TR. In the second embodiment as well, as in the first embodiment, the difference between the calculated value CV1 of the index IN1 and the calculated value CV2 of the index IN1 can be used as the index IN2.

In the second embodiment, next, in step S14, unlike the first embodiment, the fourth calculation unit 14 (see FIG. 1) is subjected to the first calculation unit 11 in step S11 as shown in FIG. The wheel load calculation value CL1 of the cumulative wheel load WL1 as an index representing the plurality of wheel loads calculated in each of the plurality of section SCs, and the wheel load calculation value CL1 of the third calculation unit 13 in step S13 in each of the plurality of section SCs, respectively. Based on the calculated values CV3 of the plurality of index IN2s calculated, the regression equation RE2 showing the relationship between the cumulative wheel load WL1 and the index IN2 is calculated. In addition, FIG. 10 schematically shows a graph in which the horizontal axis is the cumulative wheel load P and the vertical axis is the difference Δσ of the standard deviation.

As described above, as an index IN1, when using the standard deviation of the measured values of a plurality of track displacement TR, as shown in FIG. 10, in step S14, the cumulative wheel load WL1 (cumulative wheel load P ₁₎ standard deviation The regression equation RE2 is calculated from the difference Δσ ₁₂ .

As shown in FIG. 10, in a graph in which the horizontal axis is the cumulative wheel load P and the vertical axis is the difference Δσ of the standard deviation, the wheel load calculation value CL1 of the cumulative wheel load WL1 calculated for each of the plurality of section SCs is shown. plot the set data of the calculated value of (cumulative wheel load _{P 1)} indicative IN2 CV3 (standard deviation difference .DELTA..sigma _12). Then, the regression calculation using the regression equation RE2 represented by the following equation (Equation 22) or the following equation (Equation 23) as an example of the following equation (Equation 22) is performed so that the correlation coefficient becomes maximum, for example. The values of c and d are determined. By such a method, the regression equation RE2 can be calculated.

In the second embodiment, then, in step S15, unlike the first embodiment, the fifth calculation unit 15 (see FIG. 1) is a cumulative ring in each of the plurality of section SCs, as shown in FIG. a wheel load calculating values of heavy WL1 CL1 (cumulative wheel load _{P 1),} and the regression equation RE2, on the basis to calculate a predicted value PV1 index IN2, the predicted value PV1 of the calculated index IN2, the indicator IN2 The correction coefficient CF1 indicating the relationship with the calculated value CV3 is calculated. Note that FIG. 11 schematically shows a graph in which the horizontal axis is the cumulative wheel load P and the vertical axis is the difference Δσ of the standard deviation, as in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacements TR are used as the index IN1, in step S15, the fifth calculation unit 15 calculates the correction coefficient CF1 of the standard deviation difference Δσ _12. Become.

Preferably, as shown in FIG. 11, the fifth calculation unit 15 substitutes the wheel load calculation value CL1 as the cumulative wheel load WL1 into the regression equation RE2 in each of the plurality of section SCs in step S15. The predicted value PV1 of the index IN2 is calculated. In addition, preferably, as shown in FIG. 11, in step S15, in step S15, the ratio of the calculated value CV3 of the index IN2 to the predicted value PV1 of the calculated index IN2 in each of the plurality of section SCs. The correction coefficient CF1 is calculated. Further, assuming that the correction coefficient CF ₁ is expressed as the correction coefficient γ ₁ , the correction coefficient γ ₁ is expressed by the above equation (Equation 4) as in the first embodiment.

When the regression equation RE2 is expressed by the above equation (Equation 23), the calculated value CV3 (standard deviation difference Δσ ₁₂ ) of the index IN2 satisfies the correction equation CE4 expressed by the following equation (Equation 24). become. In FIG. 11, the regression equation RE2 is indicated by a solid line, and the correction equation CE4 is indicated by a broken line.

In the second embodiment, next, in step S16, unlike the first embodiment, the sixth calculation unit 16 calculates the second in step S12 in each of the plurality of section SCs, as shown in FIG. Step based on the wheel load calculated value CL2 of the cumulative wheel load WL1 calculated by the unit 12, the regression equation RE2, and the calculated value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15. In S12, the second calculation unit 12 calculates the predicted value PV2 of the index IN3 indicating the degree of change in the orbital displacement TR after the orbital displacement TR is measured by the measurement unit 22.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S16, the sixth calculation unit 16 predicts the differences of the standard deviations of the second and third times. .. Further, assuming that the predicted value PV2 of the index IN3 is expressed as the predicted value Δσ ₂ ^* of the difference between the second and third standard deviations, the predicted value PV2 of the index IN3 is expressed by the above equation (Equation 6). Further, preferably, in step S16, the sixth calculation unit 16 substitutes the wheel load calculation value CL2 as the cumulative wheel load WL1 into the regression equation RE2 in each of the plurality of section SCs, whereby the predicted value of the index IN2 is obtained. The predicted value PV2 of the index IN3 is calculated by calculating PV3 and multiplying the calculated predicted value PV3 of the index IN2 by the correction coefficient CF1.

The orbital displacement prediction method of the second embodiment replaces the regression equation RE1 showing the relationship between the index IN1 indicating the variation in the measured values of the plurality of orbital displacement TRs and the index IN2 indicating the degree of change in the orbital displacement TRs. The same as in the first embodiment, except that the regression equation RE2, which indicates the relationship between the index indicating the wheel load in each of the plurality of section SCs and the index IN2 indicating the degree of change in the orbital displacement TR, is used. can do. Therefore, even in the orbital displacement prediction method using the orbital displacement prediction system of the second embodiment, for example, even if the historical data of the orbital displacement is small and insufficient, the future orbital displacement can be predicted with high accuracy. It has the same effect as the orbital displacement prediction method using the orbital displacement prediction system of the first aspect.

Further, in the second embodiment, a plurality of regression equations RE1 indicating the relationship between the index IN1 indicating the variation in the measured values of the plurality of orbital displacement TRs and the index IN2 indicating the degree of change in the orbital displacement TRs are used. Step S17 as in the first embodiment, except that the regression equation RE2 indicating the relationship between the index representing the wheel load in each of the sections SC and the index IN2 indicating the degree of change in the orbital displacement TR is used. To step S20 can be performed.

That is, in the second embodiment, after the second calculation unit 12 measures the track displacement TR by the measurement unit 22 in step S12, in step S17, the seventh calculation unit 17 (see FIG. 1) performs the embodiment. Unlike 1, the track displacement TR is measured again at a plurality of measurement position MPs in each of the plurality of section SCs, and the index IN1 and the cumulative wheel load WL1 are calculated again.

Further, in the second embodiment, then, in step S18, the eighth calculation unit 18 (see FIG. 1) is, as shown in FIG. 7, each of the plurality of section SCs as in the first embodiment. Then, based on the calculated value CV2 of the index IN1 calculated by the second calculation unit 12 in step S12 and the calculated value CV5 of the index IN1 calculated by the seventh calculation unit 17 in step S17, step S12 Changes in the orbital displacement TR after the second calculation unit 12 measures the orbital displacement TR by the measurement unit 22 and before the seventh calculation unit 17 measures the orbital displacement TR by the measurement unit 22 in step S17. The index IN4 indicating the degree of is calculated.

As described above, when the standard deviations of the measured values of the plurality of orbital displacement TRs are used as the index IN1, in step S18, the differences of the second and third standard deviations are calculated. Further, as the calculated value CV6 of the index IN4, the calculated value of the difference Δσ ₂₃ of the second and third standard deviations can be used. Further, the difference Δσ ₂₃ of the second and third standard deviations is calculated by the above equation (Equation 7).

Further, in the second embodiment, then, in step S19, the ninth calculation unit 19 (see FIG. 1) is in each of the plurality of section SCs as in the first embodiment, as shown in FIG. , The correction coefficient CF2 indicating the relationship between the predicted value PV3 of the index IN2, the calculated value CV6 of the index IN4 calculated by the eighth calculation unit 18 in step S18, and the correction coefficient CF1 is calculated. Note that FIG. 12 schematically shows a graph in which the horizontal axis is the cumulative wheel load P and the vertical axis is the difference Δσ of the standard deviation, as in FIG.

As described above, when the standard deviations of the measured values of the plurality of orbital displacements TR are used as the index IN1, in step S19, the ninth calculation unit 19 calculates the correction coefficient CF2 of the standard deviation difference Δσ _23. Become.

Preferably, as shown in FIG. 12, the ninth calculation unit 19 calculates the index IN4 with respect to the product of the predicted value PV3 of the index IN2 and the correction coefficient CF1 in each of the plurality of sections SC in step S19. The correction coefficient CF2, which is the ratio of CV6, is calculated. Further, assuming that the correction coefficient CF ₂ is expressed as the correction coefficient γ ₂ , the correction coefficient γ ₂ is expressed by the above equation (Equation 8).

When the regression equation RE2 is expressed by the above equation (Equation 23), the calculated value CV6 (standard deviation difference Δσ ₂₃ ) of the index IN2 satisfies the correction equation CE5 expressed by the following equation (Equation 25). become. In FIG. 12, the regression equation RE2 is indicated by a solid line, and the correction equation CE4 and the correction equation CE5 are indicated by a broken line.

However, in step S19, unlike the first embodiment, the cumulative wheel load WL1 is set in the regression equation RE2, and the wheel load calculated value CL2 (cumulative wheel) of the cumulative wheel load WL1 calculated by the second calculation unit 12 in step S12. by substituting the heavy _{P 2),} to calculate the predicted value PV3 index IN2.

Further, in the second embodiment, next, in step S20, the tenth calculation unit 20 is calculated by the seventh calculation unit 17 in step S17 in each of the plurality of section SCs, unlike the first embodiment. and a wheel load calculating values CL3 of the cumulative wheel load WL1 (cumulative wheel load _{P 3),} and the regression equation RE2, the calculated value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15, to step S19 The change in the orbital displacement TR after the 7th calculation unit 17 measures the orbital displacement TR by the measurement unit 22 in step S17 based on the calculated value CV7 of the correction coefficient CF2 calculated by the 9th calculation unit 19. The predicted value PV4 of the index IN5 indicating the degree of is calculated.

As described above, when the standard deviation of the measured values of the plurality of orbital displacement TRs is used as the index IN1, in step S20, the tenth calculation unit 20 predicts the difference of the standard deviations of the third and fourth times. .. Further, assuming that the predicted value PV4 of the index IN5 is expressed as the predicted value Δσ ₃ ^* of the difference between the third and fourth standard deviations, the predicted value PV4 of the index IN5 is expressed by the above equation (Equation 10).

By repeating steps S17 to S20, the acquisition of the orbital displacement data and the update of the correction coefficient are repeated, and the orbital displacement can be predicted with higher accuracy. Therefore, even in the track displacement prediction method using the track displacement prediction system of the second embodiment, the conditions such as the track structure, the vehicle, or the operation are the same as the track displacement prediction method using the track displacement prediction system of the first embodiment. It is possible to realize an orbital displacement prediction method and an orbital displacement prediction system that predict future orbital displacements that can respond to changes in the above.

Since it is sufficient that the same calculation method can be used for each of the plurality of section SCs as the calculation method of the index representing the wheel weight, the index representing the wheel weight is not limited to the cumulative wheel weight, but is cumulative. The wheel load calculated by various calculation methods other than the wheel load calculation method can be used. Further, as described in the following modification, an index representing the rail pressure can be used instead of the index representing the wheel load.

<Modification example of track displacement prediction system and track displacement prediction method>
As described above, as a modification of the track displacement prediction system and the track displacement prediction method of the second embodiment, a case where an index representing the rail pressure is used instead of the index representing the wheel load will be described. In addition, except that the index representing the rail pressure is used instead of the index representing the wheel load, the track displacement prediction system and the track displacement prediction method of this modification are the track displacement prediction system and the track displacement of the second embodiment. Since it can be the same as the prediction method, detailed description and illustration thereof will be omitted.

In this modification, in step S11, as in the second embodiment, the first calculation unit 11 (see FIG. 1) has the length of the orbit RA in each of the plurality of section SCs as shown in FIG. The orbital displacement TR is measured at a plurality of measurement position MPs different from each other along the direction, and a plurality of orbital displacement TRs are measured based on the measured values of the plurality of orbital displacement TRs measured at each of the plurality of measurement position MPs. The index IN1 indicating the variation of the values is calculated.

On the other hand, in the present modification, in step S11, unlike the second embodiment, the first calculation unit 11 is an index based on the measured values of the plurality of orbital displacement TRs measured at each of the plurality of measurement position MPs. In addition to IN1, the rail pressure in each of the plurality of section SCs is calculated as an index showing the rail pressure in each of the plurality of section SCs instead of the index showing the wheel load. When an index representing the rail pressure is used instead of the index representing the wheel load, the rail pressure is calculated according to the following formula (Equation 26) to the following formula (Equation 31).

First, when the rail pressure is expressed as the rail pressure _Pr (kN), the rail pressure _Pr is the cumulative wheel load P described in the second embodiment described above, the sleeper laying interval α (m), and continuous. It is represented by the following (Equation 26) using a beam model on an elastic floor.

The variable β in the above equation (Equation 26) is expressed using the following equations (Equation 27) to the following (Equation 30).

The variables in the above equation (Equation 27) to the above equation (Equation 30) are the variables shown below.
k: Rail support spring constant per unit length (MN / m ² )
EI _x : Vertical bending rigidity of rail (MN ・ m ² )
D _P: track pad spring constant (= 110MN / m)
D _B: track bed spring rate (MN / m)
D _S: roadbed spring rate (MN / m)
h _B : Roadbed thickness (mm)
K ₃₀ : Roadbed strength (MN / m ³ )
S _T: sleeper bottom area ^(m 2)

When an elastic sleeper is used as the sleeper, the rail support spring constant k'per unit length calculated by the following formula (Equation 31) is used instead of the rail support spring constant k per unit length. Use.

The variables in the above equation (Equation 31) are the variables shown below.
D _M : Elastic material spring constant (MN / m)

As shown in the equation (Expression 26), the rail pressure P _r is dependent on the cumulative wheel load P, as described in the second embodiment described above, the cumulative wheel load P is calculated value CV1 of the index IN1 ( It depends on the standard deviation σ ₁ ). Therefore, if the rail pressure _{P r} of the rail pressure _{P r1} obtained by first calculating section 11 at step S11 measures the orbital displacement TR by measuring unit 22, the rail pressure _{P r1} is calculated value CV1 of the index IN1 ( It depends on the standard deviation σ ₁ ).

In this modification, after the first calculation unit 11 measures the track displacement TR by the measurement unit 22 in step S11, in step S12, the second calculation unit 12 (see FIG. 1) is in the same manner as in the second embodiment. , As shown in FIG. 4, in each of the plurality of section SCs, the orbital displacement TR is measured again by the measuring unit 22 at a plurality of measuring position MPs, and the index IN1 is calculated again.

On the other hand, in the present modification, in step S12, unlike the second embodiment, the second calculation unit 12 replaces the index indicating the wheel load with the index IN1 and the rail pressure in each of the plurality of section SCs. as an index representing the calculated rail pressure P _r at each of the plurality of sections SC again. Calculating the rail pressure _{P r} at step S12, may be similar to the calculation of the rail pressure _{P r} at step S11. Therefore, if the rail pressure _{P r} obtained by measuring the track displacement TR by the second calculating unit 12 is the measurement unit 22 at step S12 and the rail pressure _{P r2,} rail pressure _{P r2} is calculated value of the index IN1 CV2 ( It depends on the standard deviation σ ₂ ).

In this modified example, next, in step S13, in the same manner as in the second embodiment, in the third calculation unit (see FIG. 1), in step S11, the first calculation unit 11 causes the orbital displacement TR by the measurement unit 22. The index IN2 indicating the degree of change in the orbital displacement TR after the measurement and before the second calculation unit 12 measures the orbital displacement TR by the measurement unit 22 in step S12 is calculated.

In this modification, next, in step S14, the same can be applied to the second embodiment except that the index representing the rail pressure is used instead of the index representing the wheel load. Then, in step S14, the fourth calculation unit 14 (see FIG. 1) uses the rail pressure as an index representing the plurality of rail pressures calculated by the first calculation unit 11 in each of the plurality of section SCs in step S11. index calculated value of P _r (corresponding to wheel loads calculated value CL1 in Figure 10), the calculated value CV3 plurality of indices IN2 calculated respectively by the third calculation unit 13 at step S13 in each of a plurality of sections SC , A regression equation RE2 showing the relationship between the index representing the rail pressure and the index IN2 is calculated (see FIG. 10).

In this modification, next, in step S15, the same can be applied to the second embodiment except that an index representing the rail pressure is used instead of the index representing the wheel load. In step S15, the fifth calculating section 15 (see FIG. 1) is, at each of a plurality of sections SC, index calculation value of the rail pressure _{P r} (corresponding to wheel loads calculated value CL1 in Figure 11), regression equation Based on RE2, the predicted value PV1 of the index IN2 is calculated, and the correction coefficient CF1 indicating the relationship between the calculated predicted value PV1 of the index IN2 and the calculated value CV3 of the index IN2 is calculated (see FIG. 11). ).

In this modification, next, in step S16, the same can be applied to the second embodiment except that an index representing the rail pressure is used instead of the index representing the wheel load. In step S16, the sixth calculation unit 16 (see FIG. 1) is, at each of a plurality of sections SC, index calculation value of the rail pressure _{P r} which is calculated by the second calculating unit 12 in step S12 (FIG. 11 The second calculation unit in step S12 based on the calculation value CL2 of the wheel load), the regression equation RE2, and the calculation value CV4 of the correction coefficient CF1 calculated by the fifth calculation unit 15 in step S15. 12 calculates the predicted value PV2 of the index IN3 indicating the degree of change in the track displacement TR after the track displacement TR is measured by the measuring unit 22 (see FIG. 11).

The track displacement prediction method of this modification can be the same as that of the second embodiment except that the index representing the rail pressure is used instead of the index representing the wheel load. Therefore, even in the orbital displacement prediction method using the orbital displacement prediction system of this modification, for example, even if the historical data of the orbital displacement is small and insufficient, the future orbital displacement can be predicted with high accuracy. It has the same effect as the orbital displacement prediction method using the orbital displacement prediction system of.

In this modification, steps S17 to S20 can be performed in the same manner as in the second embodiment, except that the index representing the rail pressure is used instead of the index representing the wheel load (see FIG. 12). ..

By repeating steps S17 to S20, the acquisition of the orbital displacement data and the update of the correction coefficient are repeated, and the orbital displacement can be predicted with higher accuracy. Therefore, even in the track displacement prediction method using the track displacement prediction system of this modified example, changes in conditions such as track structure, vehicle, or operation are performed as in the track displacement prediction method using the track displacement prediction system of the second embodiment. It is possible to realize a track displacement prediction method and a track displacement prediction system that predict future track displacements.

Although the invention made by the present inventor has been specifically described above based on the embodiment thereof, the present invention is not limited to the embodiment and can be variously modified without departing from the gist thereof. Needless to say.

Within the scope of the idea of the present invention, those skilled in the art can come up with various modified examples and modified examples, and it is understood that these modified examples and modified examples also belong to the scope of the present invention.

For example, a person skilled in the art appropriately adds, deletes, or changes the design of each of the above-described embodiments, or adds, omits, or changes the conditions of the process of the present invention. As long as it has a gist, it is included in the scope of the present invention.

The present invention is effective when applied to a track displacement prediction method and a track displacement prediction system for predicting track displacement.

10 Orbital displacement prediction system 11 1st calculation unit 12 2nd calculation unit 13 3rd calculation unit 14 4th calculation unit 15 5th calculation unit 16 6th calculation unit 17 7th calculation unit 18 8th calculation unit 19 9th calculation unit 20 10th calculation unit 21 Calculation unit 22 Measurement unit 23 Control unit CE1 to CE5 Correction formula CF1, CF2 Correction coefficient CL1 to CL3 Wheel load calculation value CV1 to CV7 Calculation value IN1 to IN5 Index MP Measurement position PV1 to PV4 Predicted value RA Orbit RE1, RE2 Regression type SC, SC1 to SC5 Section TR, TR1 to TR3 Orbital displacement WL1 Cumulative wheel load

Claims (13)

In the orbital displacement prediction method for predicting the orbital displacement in each of the plurality of sections in the orbit including a plurality of sections arranged along the length direction of the orbit.
(A) In each of the plurality of sections, the orbital displacement is measured at a plurality of measurement positions different from each other along the length direction, and the plurality of the orbital displacements measured at each of the plurality of measurement positions. Steps to calculate the first index representing the variation of measured values,
(B) A step of measuring the track displacement in the step (a), then measuring the track displacement again at the plurality of measurement positions in each of the plurality of sections, and recalculating the first index.
(C) In each of the plurality of sections, the first calculated value of the first index calculated in the step (a) and the second calculation of the first index calculated in the step (b). A step of calculating a second index indicating the degree of change in the orbital displacement before measuring the orbital displacement in the step (b) based on the value.
(D) A plurality of the first calculated values calculated in each of the plurality of sections, and a third of the plurality of the second indexes calculated in each of the plurality of sections in the step (c). A step of calculating a regression equation showing the relationship between the first index and the second index based on the calculated value.
(E) In each of the plurality of sections, the first predicted value of the second index is calculated based on the first calculated value and the regression equation, and the calculated first predicted value is used. Step of calculating the first correction coefficient indicating the relationship with the third calculated value,
(F) In each of the plurality of sections, based on the second calculated value, the regression equation, and the fourth calculated value of the first correction coefficient calculated in the step (e). (B) A step of calculating a second predicted value of a third index indicating the degree of change in the orbital displacement after measuring the orbital displacement in the step.
A method for predicting orbital displacement. In the orbital displacement prediction method according to claim 1,
In the step (e), the first predicted value is calculated and calculated by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections. An orbital displacement prediction method for calculating the first correction coefficient, which is the ratio of the third calculated value to the predicted value. In the orbital displacement prediction method according to claim 2,
In the step (f), the third predicted value of the second index is calculated and calculated by substituting the second calculated value as the first index into the regression equation in each of the plurality of sections. An orbital displacement prediction method for calculating the second predicted value by multiplying the third predicted value by the first correction coefficient. In the orbital displacement prediction method according to claim 3,
(G) A step of measuring the track displacement in the step (b), then measuring the track displacement again at the plurality of measurement positions in each of the plurality of sections, and recalculating the first index.
(H) In each of the plurality of sections, in the step (g), based on the second calculated value and the fifth calculated value of the first index calculated in the step (g). A step of calculating a fourth index indicating the degree of change in the orbital displacement before measuring the orbital displacement,
(I) The relationship between the third predicted value, the sixth calculated value of the fourth index calculated in the step (h), and the first correction coefficient is shown in each of the plurality of sections. Steps to calculate the second correction factor,
(J) In each of the plurality of sections, the fifth calculated value, the regression equation, the fourth calculated value, and the seventh calculated value of the second correction coefficient calculated in the step (i). Based on the above, the step of calculating the fourth predicted value of the fifth index indicating the degree of change in the orbital displacement after the orbital displacement was measured in the step (g).
A method for predicting orbital displacement. In the orbital displacement prediction method according to claim 4,
In the step (i), the second correction coefficient, which is the ratio of the sixth calculated value to the product of the third predicted value and the first correction coefficient, is calculated in each of the plurality of sections. Orbital displacement prediction method. In the orbital displacement prediction method according to claim 1,
In the step (e), the first predicted value is calculated and calculated by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections. An orbital displacement prediction method for calculating the first correction coefficient, which is the difference between the predicted value and the third calculated value. In the orbital displacement prediction method for predicting the orbital displacement in each of the plurality of sections in the orbit including a plurality of sections arranged along the length direction of the orbit.
(A) In each of the plurality of sections, the orbital displacement is measured at a plurality of measurement positions different from each other along the length direction, and the plurality of the orbital displacements measured at each of the plurality of measurement positions. A step of calculating a first index representing the variation of the measured values of the plurality of track displacements and a second index representing the wheel load or the rail pressure in each of the plurality of sections based on the measured values.
(B) After measuring the track displacement in the step (a), the track displacement is measured again at the plurality of measurement positions in each of the plurality of sections, and the first index and the second index are used. Steps to recalculate,
(C) In each of the plurality of sections, the first calculated value of the first index calculated in the step (a) and the second calculation of the first index calculated in the step (b). A step of calculating a third index indicating the degree of change in the orbital displacement before measuring the orbital displacement in the step (b) based on the value.
(D) The first index calculated value of the plurality of second indexes calculated in each of the plurality of sections in the step (a), and each of the plurality of sections in the step (c). A step of calculating a regression equation showing the relationship between the second index and the third index based on the calculated third calculated values of the third index.
(E) In each of the plurality of sections, the first predicted value of the third index is calculated based on the first index calculated value and the regression equation, and the calculated first predicted value is used. , The step of calculating the first correction coefficient indicating the relationship with the third calculated value,
(F) In each of the plurality of sections, the second index calculation value of the second index calculated in the step (b), the regression equation, and the second index calculated in the step (e). 1 A step of calculating a second predicted value of a fourth index indicating the degree of change in the orbital displacement after measuring the orbital displacement in step (b) based on the fourth calculated value of the correction coefficient. ,
A method for predicting orbital displacement. In a track displacement prediction system that predicts track displacement in each of the plurality of sections in the track including a plurality of sections arranged along the length direction of the track.
In each of the plurality of sections, the orbital displacement is measured at a plurality of measurement positions different from each other along the length direction, and the measured values of the plurality of orbital displacements measured at each of the plurality of measurement positions are measured. The first calculation unit that calculates the first index that represents the variation, and
After the track displacement is measured by the first calculation unit, the track displacement is measured again at the plurality of measurement positions in each of the plurality of sections, and the first index is calculated again with the second calculation unit. ,
In each of the plurality of sections, based on the first calculated value of the first index calculated by the first calculation unit and the second calculated value of the first index calculated by the second calculation unit. A third calculation unit that calculates a second index indicating the degree of change in the orbital displacement before the orbital displacement is measured by the second calculation unit.
A plurality of the first calculated values calculated in each of the plurality of sections, and a plurality of third calculated values of the second index calculated in each of the plurality of sections by the third calculation unit. A fourth calculation unit that calculates a regression equation showing the relationship between the first index and the second index based on
In each of the plurality of sections, the first predicted value of the second index is calculated based on the first calculated value and the regression equation, and the calculated first predicted value and the third The fifth calculation unit that calculates the first correction coefficient indicating the relationship between the calculated value and
In each of the plurality of sections, the second calculation unit is based on the second calculation value, the regression equation, and the fourth calculation value of the first correction coefficient calculated by the fifth calculation unit. The sixth calculation unit that calculates the second predicted value of the third index indicating the degree of change in the orbital displacement after the orbital displacement is measured by
The orbital displacement prediction system. In the orbital displacement prediction system according to claim 8,
The fifth calculation unit calculates the first predicted value by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections, and the first calculated value is calculated. An orbital displacement prediction system that calculates the first correction coefficient, which is the ratio of the third calculated value to the predicted value. In the orbital displacement prediction system according to claim 9,
The sixth calculation unit calculates and calculates the third predicted value of the second index by substituting the second calculated value as the first index into the regression equation in each of the plurality of sections. An orbital displacement prediction system that calculates the second predicted value by multiplying the third predicted value by the first correction coefficient. In the orbital displacement prediction system according to claim 10,
After the track displacement is measured by the second calculation unit, the track displacement is measured again at the plurality of measurement positions in each of the plurality of sections, and the first index is calculated again with the seventh calculation unit. ,
In each of the plurality of sections, the orbital displacement is measured by the 7th calculation unit based on the 2nd calculated value and the 5th calculated value of the 1st index calculated by the 7th calculation unit. The eighth calculation unit that calculates the fourth index showing the degree of change in the orbital displacement before the
A second correction coefficient indicating the relationship between the third predicted value, the sixth calculated value of the fourth index calculated by the eighth calculation unit, and the first correction coefficient in each of the plurality of sections. 9th calculation unit to calculate
Based on the fifth calculated value, the regression equation, the fourth calculated value, and the seventh calculated value of the second correction coefficient calculated by the ninth calculation unit in each of the plurality of sections. The tenth calculation unit that calculates the fourth predicted value of the fifth index indicating the degree of change in the orbital displacement after the orbital displacement is measured by the seventh calculation unit.
The orbital displacement prediction system. In the orbital displacement prediction system according to claim 11,
The ninth calculation unit calculates the second correction coefficient, which is the ratio of the sixth calculated value to the product of the third predicted value and the first correction coefficient, in each of the plurality of sections. Orbital displacement prediction system. In the orbital displacement prediction system according to claim 8,
The fifth calculation unit calculates the first predicted value by substituting the first calculated value as the first index into the regression equation in each of the plurality of sections, and the first calculated value is calculated. An orbital displacement prediction system that calculates the first correction coefficient, which is the difference between the predicted value and the third calculated value.

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