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Digital twin, physics-based model, and machine learning applied to damage detection in structures

TG Ritto, FA Rochinha

arXiv:2005.14360v3eess.SP

TL;DR

The paper addresses how to construct a digital twin for structural damage detection while combining interpretable physics-based modeling with machine-learning speed. It uses stochastic physics-based simulations to train a classifier, finding that accuracy varies with scenario and that the classifier enables fast real-time evaluation. The framework is constrained by physics-based computational cost and reduced accuracy under changed operational conditions.

  • Problem

    The paper examines how digital twins can organize models, uncertainty, and asset data for structural damage detection and real-time engineering decisions.

  • Method

    A stochastic discrete physics-based model generates damage scenarios and trains a machine-learning classifier that serves as the digital twin.

  • Results

    The quadratic-discriminant classifier’s accuracy decreases with fewer sensors, less damage, fewer training points, greater uncertainty, and more noise, while machine learning enables fast evaluation.

  • Takeaways & Limitations

    The physics-based model provides interpretability and explores damage scenarios, while the trained classifier supports fast real-time operation.

  • Takeaways & Limitations

    Physics-based models can have high computational cost, and classifier accuracy drops when applied across different operational conditions.

Abstract

from arXiv · show

This work is interested in digital twins, and the development of a simplified framework for them, in the context of dynamical systems. Digital twin is an ingenious concept that helps on organizing different areas of expertise aiming at supporting engineering decisions related to a specific asset; it articulates computational models, sensors, learning, real time analysis, diagnosis, prognosis, and so on. In this framework, and to leverage its capacity, we explore the integration of physics-based models with machine learning. A digital twin is constructed for a damaged structure, where a discrete physics-based computational model is employed to investigate several damage scenarios. A machine learning classifier, that serves as the digital twin, is trained with data taken from a stochastic computational model. This strategy allows the use of an interpretable model (physics-based) to build a fast digital twin (machine learning) that will be connected to the physical twin to support real time engineering decisions. Different classifiers (quadratic discriminant, support vector machines, etc) are tested, and different model parameters (number of sensors, level of noise, damage intensity, uncertainty, operational parameters, etc) are considered to construct datasets for the training. The accuracy of the digital twin depends on the scenario analyzed. Through the chosen application, we are able to emphasize each step of a digital twin construction, including the possibility of integrating physics-based models with machine learning. The different scenarios explored yield conclusions that might be helpful for a large range of applications.

1 Introduction

The paper frames digital twins as virtual representations of physical assets and investigates integrating interpretable physics-based models with fast, data-adapted machine learning for structural damage detection. It develops a stochastic-model-based classifier and emphasizes the ingredients and construction steps needed to support real-time engineering decisions.

  • Digital twins are virtual representations of specific physical assets that connect collected asset data with digital models.
  • Physics-based models provide physical interpretability, whereas machine learning models adapt well to data and real-time applications.
  • The analyzed digital twin tracks a simple lumped-parameter structure using a computational model, uncertainty quantification, and data-based calibration or updating.
  • The paper contributes a structural-dynamics digital-twin framework for damage detection and assesses physics-based and machine-learning model integration.
  • A stochastic physics-based computational model generates different damage scenarios to train a machine-learning classifier serving as the digital twin.
  • The resulting classifier is intended to connect with the physical twin and support real-time engineering decisions.

2 A Digital twin framework

The proposed digital-twin framework coordinates computational modeling, uncertainty treatment, and calibration with measurements from a specific physical asset. It links physical and virtual systems so predictions can support operational decisions while confidence is assessed stochastically.

  • Measurements from the physical twin calibrate or update the digital twin, whose predictions support decisions about physical-twin operation.
  • Digital-twin applications include actuator information, alarms, diagnosis, prognosis, system design, and sensor or actuator placement.
  • The framework treats a digital twin as more than a computational model: it also incorporates uncertainties, asset data, updating, and lifecycle tracking.
  • Figure 1 combines a computational model integrating physics-based and machine-learning models with a stochastic layer for uncertainties.
  • Three mandatory framework ingredients are a computational model, uncertainty quantification, and calibration using laboratory and field data.
  • Prediction confidence should be calculated through stochastic analysis, while alternative uncertainty approaches such as fuzzy sets are not considered.

3 Integrating physics-based models with machine learning

The paper combines physics-based simulation with machine learning to balance interpretability and computational speed in digital-twin applications. Physics-based models support scenario exploration but can be costly, while machine-learning models are fast yet generally limited outside their training domain.

  • Data-driven models require calibration or training and validation or testing, with normalization and regularization recommended depending on the problem.
  • Physics-based models use first principles and closure models, with parameters that have clear physical interpretations.
  • Physics-based models can analyze multiple new scenarios, but uncertainty, incomplete physics, and high computational cost constrain their use.
  • Machine-learning models transform inputs into outputs without physical laws, and their parameters are usually seldom physically interpretable.
  • Machine-learning models can fit experimental data and run fast, but over-fitting must be avoided and extrapolation beyond trained scenarios is limited.
  • The paper integrates both model types to leverage physics-based interpretability and machine-learning speed for digital-twin damage detection.

4 A Digital Twin to damage detection in structures

The paper develops a structural-dynamics digital twin for damage detection by combining an interpretable stochastic physics-based model with a fast machine-learning classifier. A bar-structure prototype demonstrates how measurements, uncertainty, damage simulations, and classification support diagnosis.

  • Framework and objectives: Damage detection is framed as an inverse problem mapping sensor measurements to damage presence, location, and severity.The prototype uses simulations from a physics-based model to address these three goals.
  • Framework and objectives: The prototype uses a bar structure, a discrete six-degree-of-freedom physics-based model, uncertainty quantification, and calibration with physical-twin data.The discrete model represents the physical twin and supports interpretable machine-learning tools.
  • Physics-based modeling: The deterministic computational model reproduces comparable response amplitudes, with first natural-frequency errors below 5% relative to the physical twin.A force is applied at the system’s right end, and the response is measured at the sixth degree of freedom.
  • Physics-based modeling: Introducing independent parameter uncertainties produces a stochastic model whose 95% statistical envelope more closely approaches the physical-twin response.The uncertain parameters use uniform bounds of ±5% around nominal values, with the envelope representing confidence.
  • Digital-twin construction: The stochastic physics-based model generates damage-scenario data for training a machine-learning classifier that functions as the digital twin.The dataset contains displacement features for multiple damage scenarios, including the healthy structure.
  • Digital-twin construction: Quadratic discriminant analysis performed best for the application, while the framework integrates interpretable physics-based simulation with fast machine-learning evaluation.The classifier is intended to connect with the physical twin and support real-time engineering decisions.

5 Assessing the Digital Twin

The digital twin classified structural damage accurately in the reference setting, but performance varied with damage intensity, sensing, uncertainty, noise, training data, and operating conditions.

  • 5.1 Dataset 1: 20% of damage at each spring: 93.3% accuracy was achieved by the quadratic discriminant classifier for six configurations with 20% damage scenarios.The dataset included healthy structure and damage at each of five springs, with 200 samples per configuration.
  • 5.1 Dataset 1: 20% of damage at each spring: 100% accuracy occurred for damage at springs 1 and 5, while spring 3 was hardest to locate at 78%.The healthy-structure false-positive probability was 14%, and the spring-3 false-negative probability was 19%.
  • 5.2 Dataset 2: 10% of damage at each spring: 80.3% accuracy with 10% damage was lower because reduced damage makes scenarios harder to distinguish; at d=0, all scenarios converge to the healthy case.For 10% damage, accuracy was 95% at spring 1, 90% at springs 4 and 5, and 80% at spring 3.
  • 5.3 Other datasets: further analyses: Accuracy decreased with less sensing, more noise, greater uncertainty, lower damage, and fewer training points, while force location and frequency also changed results.The stated reference accuracy was 93.3%.
  • 5.3 Other datasets: further analyses: Accuracy was higher near natural frequencies 3999 Hz and 6398 Hz, but operating near resonance was not expected.Removing sensors 3 and 5 yielded 89.5% accuracy, while removing sensors 2, 3, and 5 yielded 80.0%; sensor 1 was most informative.
  • 5.3 Other datasets: further analyses: A reference twin trained at 3800 Hz generalized poorly to different excitation frequencies, reaching 93.5% at 4000 Hz and 77.5% at 3600 Hz.Allowing frequency fluctuations improved testing at 3600 Hz to 83.0%, compared with 80.5% for fixed-frequency training.

6 Concluding remarks

The paper presents a structural-dynamics digital twin that combines computational modeling, uncertainty quantification, physical-twin calibration, and machine learning. Its accuracy declines with poorer sensing or information, while the physics-based model supports interpretability and exploration of damage scenarios.

  • Framework: The framework represents a physical asset for real-time engineering decisions using a computational model, uncertainty quantification, and calibration with physical-twin data.These are identified as three important framework ingredients.
  • Framework: A physics-based model is combined with a machine learning classifier to construct a digital twin connected to the physical counterpart.The classifier serves as the fast digital component, while the computational strategy supports the overall twin.
  • Findings: The classifier’s accuracy decreases with fewer sensors, less damage, fewer training points, greater uncertainty, and more noise.Several operational conditions were also tested for their impact on accuracy.
  • Findings: The physics-based computational model supports interpretability and enables exploration of damage scenarios that could not be assessed with the physical twin.The discrete damaged structure was used to construct the digital twin step by step.

A Elementary mass and stiffness matrices of the bar model

This appendix introduces the elementary mass and stiffness matrices for the bar model, with element length denoted by L_e.

  • A Elementary mass and stiffness matrices of the bar model: The bar model’s elementary mass and stiffness matrices are presented using the element length L_e.The supplied passage introduces these matrices but does not provide their entries.

B Mass and stiffness matrices of the computational model

This appendix presents the mass and stiffness matrices used by the computational model.

  • B Mass and stiffness matrices of the computational model: The computational model’s mass and stiffness matrices are given in this appendix.The supplied passage states their presentation without specifying the matrix entries.
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