The present application is based on, and claims priority from JP Application Serial Number 2020-047136, filed Mar. 18, 2020, the disclosure of which is hereby incorporated by reference herein in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates to a measurement method, a measurement device, a measurement system, and a measurement program.

2. Related Art

In maintaining and managing a bridge, an axle load of a large vehicle passing through the bridge is important information for predicting damage to the bridge. For axle load measurement, JP-A-2009-237805 proposes weight in motion, which is a method of continuously measuring a strain value when the vehicle passes from a strain gauge installed on a main girder of the bridge and calculating the axle load. JP-A-2009-237805 discloses a bridge-passing vehicle monitoring system that measures a vehicle weight of a vehicle passing through a bridge based on a strain waveform measured by a strain gauge arranged on a main girder of the bridge.

Specifically, in the bridge-passing vehicle monitoring system, the strain gauge is arranged, a passage timing of the axle is detected based on the strain waveform measured by the strain gauge, an inter-axle ratio of the vehicle is calculated, the calculated inter-axle ratio is compared with an inter-axle ratio calculated based on an inter-axle distance registered in an inter-axle distance database, and the inter-axle distance, a vehicle speed, and a vehicle type of the vehicle are identified. The bridge-passing vehicle monitoring system generates a strain waveform in which a reference axle load strain waveform is arranged on a time axis according to the passage timing of the axle, and calculates the axle load of each axle by comparing the reference axle load strain waveform with a strain waveform measured by the strain gauge. Then, the bridge-passing vehicle monitoring system calculates the vehicle weight by summing the axle loads of each axle.

When the vehicle travels on the bridge, the bridge floor is displaced and inclined in a width direction at the same time as the bridge floor is displaced and settled in a traveling direction of the vehicle. This means that when the vehicle passes an observation point, not only an action occurs at the observation point, but also an action occurs at other observation points. The action on each observation point changes according to the number of vehicles traveling on the bridge, a weight of each vehicle, a situation of a lane on which each vehicle travels, and the like. Therefore, in order to perform accurate measurement, it is necessary to calculate the action on the observation point when the vehicle passes through each observation point separately from other actions. The system disclosed in JP-A-2009-237805 can measure the vehicle weight of the vehicle, but the action on the observation point when a moving object such as the vehicle passes through each observation point of a structure such as the bridge cannot be calculated separately from other actions.

SUMMARY

A measurement method according to a first aspect of the present disclosure includes: a physical quantity acquisition step of acquiring, based on observation information obtained by at least one observation device that observes first to N-th observation points of a structure arranged along a second direction intersecting a first direction in which a moving object moves along the structure, physical quantities at the first to N-th observation points, N being an integer of 2 or more; and an action calculation step of calculating actions x1to xNon the first to N-th observation points based on the physical quantities at the first to N-th observation points acquired in the physical quantity acquisition step, on the assumption that, for any integer i of 1 or more and N or less and any integer j of 1 or more and N or less, when a function indicating a correlation between an action xjon a j-th observation point and an action that the action xjhas on an i-th observation point is set as yij, a physical quantity at the i-th observation point acquired in the physical quantity acquisition step is equal to a sum of values of functions yi1to yiN.

The measurement method according to the first aspect may further include: a coefficient value calculation step of acquiring physical quantities at the first to N-th observation points when a known moving object different from the moving object moves alone on the structure, and calculating a value of a coefficient of the function yijbased on the physical quantities at the first to N-th observation points.

In the measurement method according to the first aspect, the function yijmay be a polynomial function of the action xj.

In the measurement method according to the first aspect, the structure may have first to N-th paths through which the moving object is able to move, and the first to N-th observation points may be associated with the first to N-th paths.

In the measurement method according to the first aspect, the physical quantities at the first to N-th observation points acquired in the physical quantity acquisition step may be displacements or loads generated by the moving object.

In the measurement method according to the first aspect, the observation device may be an acceleration sensor.

In the measurement method according to the first aspect, the observation device may be a contact displacement meter, a ring displacement meter, a laser displacement meter, a pressure sensor, a displacement measurement device based on image processing, or a displacement measurement device based on an optical fiber.

In the measurement method according to the first aspect, the physical quantities at the first to N-th observation points acquired in the physical quantity acquisition step may be physical quantities in a third direction intersecting the first direction and the second direction.

In the measurement method according to the first aspect, the moving object may be a railroad vehicle, an automobile, a tram, a construction vehicle, or a military vehicle.

In the measurement method according to the first aspect, the structure may be a superstructure of a bridge, the superstructure may be a structure across any one of a bridge abutment and a bridge pier adjacent to each other, two adjacent bridge abutments, or two adjacent bridge piers, both end portions of the superstructure may be located at positions of the bridge abutment and the bridge pier adjacent to each other, at positions of the two adjacent bridge abutments, or at positions of the two adjacent bridge piers, and the bridge may be a road bridge or a railway bridge.

In the measurement method according to the first aspect, the structure may be a structure in which bridge weigh in motion (BWIM) functions.

A measurement device according to a second aspect of the present disclosure includes: a physical quantity acquisition unit that acquires, based on observation information obtained by at least one observation device that observes first to N-th observation points of a structure arranged along a second direction intersecting a first direction in which a moving object moves along the structure, physical quantities at the first to N-th observation points, N being an integer of 2 or more; and an action calculation unit that calculates actions x1to xNon the first to N-th observation points based on the physical quantities at the first to N-th observation points acquired by the physical quantity acquisition unit on the assumption that, for any integer i of 1 or more and N or less and any integer j of 1 or more and N or less, when a function indicating a correlation between an action xjon a j-th observation point and an action that the action xjhas on an i-th observation point is set as yij, a physical quantity at the i-th observation point acquired by the physical quantity acquisition unit is equal to a sum of values of functions yi1to yiN.

A measurement system according to a third aspect of the present disclosure includes: the measurement device according to the first aspect; and the observation device.

A non-transitory computer-readable storage medium according to a fourth aspect of the present disclosure stores a measurement program, the measurement program causing a computer to execute: a physical quantity acquisition step of acquiring, based on observation information obtained by at least one observation device that observes first to N-th observation points of a structure arranged along a second direction intersecting a first direction in which a moving object moves along the structure, physical quantities at the first to N-th observation points, N being an integer of 2 or more; and an action calculation step of calculating actions x1to xNon the first to N-th observation points based on the physical quantities at the first to N-th observation points acquired in the physical quantity acquisition step, on the assumption that, for any integer i of 1 or more and N or less and any integer j of 1 or more and N or less, when a function indicating a correlation between an action xjon a j-th observation point and an action that the action xjhas on an i-th observation point is set as yij, a physical quantity at the i-th observation point acquired in the physical quantity acquisition step is equal to a sum of values of functions yi1to yiN.

