A displacement estimation system includes: accelerometers arranged with predetermined gaps therebetween in an x-axis direction corresponding to the lengthwise direction of a bridge; and a data processing device that receives, from the accelerometers, acceleration data indicating measured values of acceleration measured by the accelerometers, and estimates, based on the acceleration values in the x-axis direction indicated by the acceleration data, the relationship between a distance from a reference position in the x-axis direction and displacement from a reference orientation in a z-axis direction. Displacement of bridge at an arbitrary position in the x-axis direction can be estimated by the data processing device. Also, for each of the positions (measurement positions) at which the accelerometers are arranged, the data processing device calculates fine fluctuation components of displacement of the bridge in the z-axis direction based on the acceleration values in the z-axis direction indicated by the acceleration data, and estimates detailed displacement of the bridge at each of the measurement positions by adding the calculated fine fluctuation components to the estimated displacement in the z-axis direction.

A measurement method includes: performing low-pass filter processing and high-pass filter processing on target data; estimating correction data; generating vibration component data, and the estimating the correction data includes: specifying a first interval, a second interval, and a third interval; generating first interval correction data, generating second interval correction data in the second interval by setting data in an interval before a first intersection point of first line data and second line data as the first line data, setting data in an interval from the first intersection point to a second intersection point of second line data and third line data as the second line data, and setting data in an interval after the second intersection point as the third line data; and generating third interval correction data.

A measurement method, includes: performing high-pass filter processing on target data, estimating correction data, and generating measurement data, and the estimating the correction data includes: specifying a first interval, a second interval, and a third interval, generating first interval correction data, generating second interval correction data in the second interval by using data before a first intersection point of first line data and second line data as the first line data, data from the first intersection point to a second intersection point of the second line data and third line data as the second line data, and data after the second intersection point as the third line data, and generating third interval correction data.

A measurement method includes: a high-pass filter processing step of performing high-pass filter processing on observation data-based velocity data including a drift noise to generate drift noise reduction data in which the drift noise is reduced; a displacement data generation step of generating displacement data by integrating the drift noise reduction data; a correction data estimation step of estimating, based on the displacement data, correction data corresponding to a difference between the displacement data and data obtained by removing the drift noise from data obtained by integrating the velocity data; and a measurement data generation step of generating measurement data by adding the displacement data and the correction data.

Method for surveying a structure (1) comprising: a) defining specific parameters of the structure (1) by discretizing it into a plurality of elements and discretizing in turn each element into nodes, b) defining specific parameters for each node including the rotations in the nodes, c) defining a number of usable sensors, d) imposing specific constraints as a function of the effective number of sensors and the mutual distances thereof, e) using an exact algorithm of the branch and bound or genetic or neural type or combinations thereof in order to calculate a solution (Si) which identifies a second plurality of (N) nodes at which to position at least one sensor and which maximizes the total of the rotations read, f) positioning the sensors (3) on the structure (1) in accordance with the solution (Si) which is produced by the step e).

A vibration measurement apparatus 10 is an apparatus for measuring vibrations of an object 30. The vibration measurement apparatus 10 includes: a surface-direction displacement calculation unit 11 configured to calculate, based on time-series images of a measurement target area that are output from an imaging apparatus 20, a displacement in a surface direction of the measurement target area; a normal-direction displacement calculation unit 12 configured to calculate a displacement in a normal direction of the measurement target area, based on the time-series images and the displacement in the surface direction of the measurement target area; and a vibration calculation unit 13 configured to calculate vibrations of the object 30, based on the calculated displacement in the surface direction of the measurement target area and the calculated displacement in the normal direction of the measurement target area.

A measurement method 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; and an action calculation step of calculating actions x.sub.1 to x.sub.N on the first to N-th observation points based on the acquired physical quantities at the first to N-th observation points, on the assumption that, when a function indicating a correlation between an action x.sub.j on a j-th observation point and an action that the action x.sub.j has on an i-th observation point is set as y.sub.ij, an acquired physical quantity at the i-th observation point is equal to a sum of values of functions y.sub.i1 to y.sub.iN.

The present invention includes a method for detecting impairments of a structure in the absence of permanent sensor systems comprising: obtaining time-varying sensor data on a user device; filtering the time-varying sensor data obtained by the user device to determine a vibration response from structural infrastructure; and estimating structural responses of the structure by comparing at least one of: dynamic (short-term) sensor data to an analytical model of the structure; or dynamic sensor data from different user devices at different points in time (long-term), to determine if there has been any significant change in the structure with time.

A damage detection apparatus 10 includes: an extraction unit 11 configured to extract measured mode information representing a mode shape of a structure that is continuously supported at three or more support points, based on a plurality of pieces of vibration information measured by sensors that are disposed at a plurality of locations of the structure; a derivation unit 12 configured to derive reference mode information representing a mode shape serving as a reference for damage evaluation of the structure, using a structure model in which a value representing strength of a coupling rotation spring is set to represent a boundary condition of an intermediate support point of the structure; and a detection unit 13 configured to calculate an index indicating a degree of similarity between the measured mode information and the reference mode information, and detect damage to the structure based on the index indicating the degree of similarity.

A measurement method includes: a high-pass filter processing step of performing high-pass filter processing on target data including a drift noise to generate drift noise reduction data in which the drift noise is reduced, a correction data estimation step of estimating, based on the drift noise reduction data, correction data corresponding to a difference between the drift noise reduction data and data obtained by removing the drift noise from the target data, and a measurement data generation step of generating measurement data by adding the drift noise reduction data and the correction data.