Analysis apparatus, analysis method, and computer program product

1 . An analysis apparatus comprising:

a plurality of sensors disposed at a plurality of sample points of a structure to be analyzed and configured to detect sensing data of the structure to be analyzed;

a display; and

one or more hardware processors configured to:

acquire the sensing data from the plurality of sensors;

acquire pieces of input data each representing a physical quantity of a corresponding one of elements, the elements being obtained by performing discretization on data including the sensing data of an analysis area of the structure to be analyzed using a finite element method (FEM);

input the pieces of input data into an estimation model that is a finite element method-Lagrangian neural network model utilizing the FEM and an energy functional, wherein the pieces of input data include at least one of sensing data of health monitoring and performance characteristics of the analysis area;

obtain pieces of output data output by the estimation model, each of the pieces of output data being a value of the energy functional representing an energy of a corresponding one of the elements;

estimate a temporal and spatial distribution of structural deformation of the structure by using the output data;

detect an abnormality in the structure by analyzing the temporal and spatial distribution of structural deformation of the structure; and

output, via the display, the temporal and spatial distribution of structural deformation and any detected abnormality.

2 . The apparatus according to claim 1 , wherein the one or more hardware processors are configured to learn the estimation model to minimize a difference between a gradient of each of the pieces of output data and correct answer data of a gradient.

3 . The apparatus according to claim 2 , wherein the one or more hardware processors are configured to learn the estimation model to minimize a difference between each of the pieces of output data and correct answer data of each of the pieces of output data.

4 . The apparatus according to claim 1 , wherein the estimation model is configured to:

input the pieces of input data at a first time point t; and

output the pieces of output data that includes a physical quantity for each of the elements at a second time point t+Δt being next to the first time point t.

5 . The apparatus according to claim 1 , wherein

the energy functional is an energy functional used for analysis of continuum dynamics, and

the energy functional represents, with respect to each of the elements, energy calculated by stored energy, loss energy, and a given workload.

6 . The apparatus according to claim 1 , wherein

the energy functional is an energy functional used for electromagnetic field analysis, and

the energy functional represents, with respect to each of the elements, energy calculated by exothermic energy and a workload caused by an inductive current.

7 . The apparatus according to claim 1 , wherein

the energy functional is an energy functional used for coupled analysis of a structure and a magnetic field, and

the energy functional represents, with respect to each of the elements, energy calculated by elastic strain energy, kinetic energy, dissipation energy, and a workload caused by an eddy current.

8 . The apparatus according to claim 1 , wherein

the energy functional is an energy functional used for analysis of a phase transition phenomenon, and

the energy functional represents, with respect to each of the elements, energy calculated by superconductive energy, energy caused by a magnetic field, and interaction energy.

9 . The apparatus according to claim 1 , wherein

the energy functional is an energy functional used for analysis of electron density and hole density, and

the energy functional represents, with respect to each of the elements, energy calculated by a chemical potential, defect energy, elastic strain energy, gradient energy, crystallographic energy, and a workload from external stress for each of the elements.

10 . The apparatus according to claim 1 , wherein the one or more hardware processors are configured to calculate, from the pieces of output data, an index representing an abnormality of the analysis area.

11 . An analysis method implemented by a computer, the method comprising:

acquiring sensing data from plurality of sensors disposed at a plurality of sample points of a structure to be analyzed;

acquiring pieces of input data each representing a physical quantity of a corresponding one of elements, the elements being obtained by performing discretization on data including the sensing data of an analysis area of the structure to be analyzed using a finite element method (FEM);

inputting the pieces of input data into an estimation model that is a finite element method-Lagrangian neural network model utilizing the FEM and an energy functional, wherein the pieces of input data include at least one of sensing data of health monitoring and performance characteristics of the analysis area;

obtaining pieces of output data output by the estimation model, each of the pieces of output data being a value of the energy functional representing an energy of a corresponding one of the elements;

estimating a temporal and spatial distribution of structural deformation of the structure by using the output data;

detecting an abnormality in the structure by analyzing the temporal and spatial distribution of structural deformation of the structure; and

outputting, via a display, the temporal and spatial distribution of structural deformation and any detected abnormality.

12 . A computer program product comprising a non-transitory computer-readable recording medium on which an executable program is recorded, the program instructing a computer to:

acquire sensing data from plurality of sensors disposed at a plurality of sample points of a structure to be analyzed;

acquire pieces of input data each representing a physical quantity of a corresponding one of elements, the elements being obtained by performing discretization on data including the sensing data of an analysis area of the structure to be analyzed using a finite element method (FEM);

input the pieces of input data into an estimation model that is a finite element method-Lagrangian neural network model utilizing the FEM and an energy functional, wherein the pieces of input data include at least one of sensing data of health monitoring and performance characteristics of the analysis area;

obtain pieces of output data output by the estimation model, each of the pieces of output data being a value of the energy functional representing an energy of a corresponding one of the elements;

estimate a temporal and spatial distribution of structural deformation of the structure by using the output data;

detect an abnormality in the structure by analyzing the temporal and spatial distribution of structural deformation of the structure; and

output, via a display, the temporal and spatial distribution of structural deformation and any detected abnormality.

13 . The apparatus according to claim 1 , wherein

each of the pieces of correct answer data includes a value of the energy functional,

the value being numerically calculated using one of the pieces of input data for learning that represents the physical quantity of the corresponding one of the elements.

14 . The apparatus according to claim 1 , wherein

the estimation model is learned by pieces of learning data including pieces of correct answer data and pieces of input data for learning, each of the pieces of input data for learning representing the physical quantity of a corresponding one of the elements.