Finite element calibration for structural load identification
In various example embodiments, model calibration techniques are used to identify one or more external structural loads on a structure. Initially, material or geometry attributes of elements of a model are adjusted to minimize discrepancy between measured responses and modeled responses. Thereafter, the model is used to search for external structural loads that minimize discrepancy between the measured responses and the modeled responses. Discrepancy may be measured by an error function that looks to dynamic responses and/or static responses. A solution that minimizes discrepancy may be determined using a genetic algorithm that generates a set of proposed external structural loads, applies the set to the model to produce the modeled responses, computes an error function that measures the difference between the measured responses and the modeled responses, and evolves the solutions to minimize an error produced by the error function, with such operation proceeding until a stopping criteria is reached.
1 . A method of identifying one or more unidentified external structural loads on a structure, comprising:
accessing, by an analysis software package executing on an electronic device, a model of the structure that includes a plurality of elements;
measuring, by one or more sensors coupled to the structure during a calibration phase, responses to one or more known external structural loads;
calibrating the model of the structure, by the analysis software package during the calibration phase, by adjusting material or geometry attributes of the plurality of elements and producing modeled responses from the model to minimize discrepancy between the measured responses and the modeled responses of the calibration phase;
measuring, by the one or more sensors, during an operational phase when the structure is subject to one or more unidentified external structural loads, responses to the one or more unidentified external structural loads;
searching, by the analysis software package during the operational phase using the calibrated model of the structure, for a set of external structural loads between a minimum limit of structural load and a maximum limit of structural load that minimize a discrepancy between the measured responses to the one or more unidentified external structural loads from the one or more sensors and modeled responses produced from the calibrated model in the operational phase, wherein the searching includes:
using a genetic algorithm to generate a set of proposed external structural loads,
producing modeled responses to the set of proposed external structural loads using the calibrated model,
measuring the discrepancy between the measured responses to the one or more unidentified external structural loads and the modeled responses from the calibrated model,
using the genetic algorithm to evolve the set of proposed external structural loads over a plurality of iterations that reduce the discrepancy,
iteratively repeating the using the genetic algorithm to generate, the producing modeled responses from the calibrated model, the measuring the discrepancy, and the using the genetic algorithm to evolve until a stopping criteria is reached, and
returning the set of proposed external structural loads when the stopping criteria is reached; and
displaying on a display screen on the electronic device indications of the set of external structural loads as identified external structural loads on the structure.
2 . The method of claim 1 , wherein the discrepancy between the measured responses from the one or more sensors and the modeled responses produced from the calibrated model in the operational phase is evaluated by measuring a difference between the measured responses and the modeled responses in the operational phase, and the measured responses and the modeled responses in the operational phase each are dynamic responses, displacement responses, or strain responses.
3 . The method of claim 2 , wherein the measured responses from the one or more sensors and the modeled responses produced from the calibrated model in the operational phase each are dynamic responses, and the measuring measures a difference between measured modal shape and modeled modal shape, and a difference between measured modal frequency and modeled modal frequency.
4 . The method of claim 2 , wherein the measured responses from the one or more sensors and the modeled responses produced from the calibrated model in the operational phase each are displacement responses, and the measuring measures a difference between measured displacement and modeled displacement.
5 . The method of claim 2 , wherein the measured responses from the one or more sensors and the modeled responses produced from the calibrated model in the operational phase each are strain responses, and the measuring measures a difference between measured strain and modeled strain.
6 . The method of claim 1 , wherein the model is a finite element (FE) model and each element is represented as a node in the FE model.
7 . The method of claim 1 , wherein the set of identified external structural loads includes multiple external structural loads that each have a load magnitude and a load position.
8 . The method of claim 1 , wherein each evolved set of proposed external structural loads is a solution and the discrepancy between the measured responses to the one or more unidentified external structural loads and the modeled responses from the calibrated model is an error, and the stopping criteria is a maximum number of solutions, a maximum computation time or a minimum error.
9 . The method of claim 1 , further comprising:
determining, based on the displayed identified external structural loads, whether the identified external structural loads are compliant with limits for the structure to ensure safety of the structure.
10 . A system comprising:
one or more sensors coupled to a structure;
a display screen;
one or more processors; and
a memory configured to store a model of the structure that includes a plurality of elements representing discrete portions of the structure, and executable instructions for a plurality of software modules that are executable on the one or more processors, the plurality of software modules including:
an optimization module configured to use a genetic algorithm to generate a set of proposed external structural loads on the structure between a minimum limit of structural load and a maximum limit of structural load, to evolve the set of proposed external structural loads over a plurality of iterations that reduce a difference between measured responses from the one or more sensors and modeled responses from the model until a stopping criteria is reached, and to return a set of external structural loads when the stopping criteria is reached;
a calibration module configured to receive the set of proposed external structural loads and apply the set of proposed external structural loads to the model, and to receive modeled responses for the set of proposed external structural loads from the model and to receive measured responses from the one or more sensors coupled to the structure, and to measure the difference between the measured responses from the one or more sensors and the modeled responses from the model;
a model solver module configured to produce the modeled responses based on the model; and
a user interface module configured to display the set of external structural loads to a user as a set of identified external structural loads on the structure.
11 . The system of claim 10 , wherein the measured responses from the one or more sensors and the modeled responses from the model each are dynamic responses, and the calibration module measures a difference between measured modal shape and modeled modal shape, and a difference between measured modal frequency and modeled modal frequency.
12 . The system of claim 10 , wherein the measured responses from the one or more sensors and the modeled responses each are displacement responses, and the calibration module measures a difference between measured displacement and modeled displacement.
13 . The system of claim 10 , wherein the measured responses from the one or more sensors and the modeled responses from the model each are strain responses, and the calibration module measures a difference between measured strain and modeled strain.
14 . The system of claim 10 , wherein each evolved set of proposed external structural loads is a solution, and difference between the measured responses from the one or more sensors and the modeled responses from the model is an error, and the stopping criteria is a maximum number of solutions, a maximum computation time or a minimum error.
15 . A non-transitory electronic device-readable medium having executable instructions stored thereon, the instructions when executed by one or more processors being operable to:
access a model of a structure that includes a plurality of elements;
measure responses using one or more sensors coupled to the structure;
search for external structural loads between a minimum limit of structural load and a maximum limit of structural load that minimize discrepancy between the measured responses from the one or more sensors and modeled responses from the model, the search to
use a genetic algorithm to generate a set of proposed external structural loads,
apply the set of proposed external structural loads to the model to produce the modeled responses,
measure a difference between the measured responses from the one or more sensors and the modeled responses from the model, and
use the genetic algorithm to evolve the set of proposed external structural loads though a plurality of iterations to minimize difference between the measured responses and the modeled responses, the evolution to occur until a stopping criteria is reached, and the set of proposed external structural loads at the stopping criteria are returned as a set of external structural loads; and
display indications of the set of external structural loads as identified external structural loads on the structure.
16 . The non-transitory electronic device-readable medium of claim 15 , wherein the measured responses from the one or more sensors and the modeled responses from the model each are dynamic responses, and the instructions when executed measure a difference between measured modal shape and modeled modal shape, and a difference between measured modal frequency and modeled modal frequency.
17 . The non-transitory electronic device-readable medium of claim 15 , wherein the measured responses from the one or more sensors and the modeled responses from the model each are displacement responses, and the instructions when executed measure a difference between measured displacement and modeled displacement.
18 . The non-transitory electronic device-readable medium of claim 15 , wherein the measured responses from the one or more sensors and the modeled responses from the model each are strain responses, and the instructions when executed measure a difference between measured strain and modeled strain.
19 . The non-transitory electronic device-readable medium of claim 15 , wherein the model is a finite element (FE) model and each element is represented as a node in the FE model.
20 . A method of identifying one or more unidentified external structural loads on a bridge or building and ensuring safety compliance of the bridge or building, comprising:
accessing, by an analysis software package executing on an electronic device, a model of the bridge or building that includes a plurality of elements;
measuring, by one or more sensors coupled to the bridge or building during a calibration phase, responses to one or more known external structural loads on the bridge or building;
calibrating the model of the bridge or building, by the analysis software package during the calibration phase, by adjusting material or geometry attributes of the plurality of elements and producing modeled responses from the model to minimize discrepancy between the measured responses and the modeled responses of the calibration phase;
displaying on a display screen on the electronic device indications of progress of the calibration of the model of the bridge or building;
measuring, by the one or more sensors, during an operational phase when the bridge or building is subject to one or more unidentified external structural loads, responses to the one or more unidentified external structural loads;
searching, by the analysis software package during the operational phase using the calibrated model of the bridge or building, for a set of external structural loads that minimize a discrepancy between the measured responses to the one or more unidentified external structural loads from the one or more sensors and modeled responses produced from the calibrated model in the operational phase, wherein the searching includes:
generating a set of proposed external structural loads,
producing modeled responses to the set of proposed external structural loads using the calibrated model,
measuring the discrepancy between the measured responses to the one or more unidentified external structural loads and the modeled responses from the calibrated model,
evolving the set of proposed external structural loads over a plurality of iterations that reduce the discrepancy, and
iteratively repeated the generating, the producing, the measuring, and the evolving until a stopping criteria is reached,
displaying on the display screen on the electronic device indications of the set of external structural loads as identified external structural loads on the bridge or building; and
determining, based on the displayed identified external structural loads, whether the identified external structural loads are compliant with limits for the bridge or building to ensure safety of the bridge or building.