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Keywords = Bayesian parameter and damage identification

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26 pages, 4251 KB  
Article
Reliability-Aware Robust Optimization for Multi-Type Sensor Placement Under Sensor Failures
by Shenghuan Zeng, Ding Luo, Pujingru Yan, Naiwei Lu, Ke Huang and Lei Wang
Buildings 2026, 16(5), 1024; https://doi.org/10.3390/buildings16051024 - 5 Mar 2026
Viewed by 247
Abstract
In the field of structural health monitoring systems, sensors serve as the fundamental components for assessing infrastructure integrity. The rationality of their spatial configuration significantly influences the precision of structural performance assessment, the efficacy of damage detection algorithms, and the operational reliability of [...] Read more.
In the field of structural health monitoring systems, sensors serve as the fundamental components for assessing infrastructure integrity. The rationality of their spatial configuration significantly influences the precision of structural performance assessment, the efficacy of damage detection algorithms, and the operational reliability of the system throughout its designated lifecycle. A robust optimization methodology for the placement of multi-type sensors is proposed in this study, explicitly formulated to mitigate the negative impact of sensor malfunctions during long-term operation. First, a rigorous evaluation framework for sensor placement schemes is established based on Bayesian inference and the minimization of information entropy, thereby quantifying the uncertainty inherent in parameter identification. Then, a probabilistic model of sensor failure is developed utilizing the Weibull distribution to capture time-dependent reliability characteristics, combined with a modified information entropy calculation method that mathematically assimilates these failure probabilities into the optimization objective. Finally, a heuristic search strategy is employed to achieve the robust optimal placement of multi-type sensors, efficiently navigating the complex combinatorial search space. In contrast to deterministic information entropy (DIE) methodologies, which assume ideal sensor functionality, the robust information entropy (RIE) approach comprehensively accounts for the stochastic nature of sensor failures and their impact on the information content of the monitoring network, thereby significantly augmenting the robustness and redundancy of the sensor configuration. Validations utilizing a numerical frame structure and a finite element bridge model demonstrate that the RIE method effectively integrates the sensor failure probability model to yield robust optimal placement schemes, minimizing the risk of information loss and ensuring reliable structural health monitoring throughout the engineering lifecycle. Full article
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31 pages, 5918 KB  
Article
Surrogate-Based Multi-Objective Bayesian Optimization for Automated Parameter Identification in 3D Mesoscale Concrete Fatigue Modeling
by Himanshu Rana and Adnan Ibrahimbegovic
Computation 2026, 14(3), 63; https://doi.org/10.3390/computation14030063 - 2 Mar 2026
Viewed by 236
Abstract
Prediction of fatigue failure in concrete structures remains a major challenge due to progressive material degradation. Reliable prediction, therefore, requires modeling the 3D heterogeneous microstructure of concrete to explain the underlying mechanisms governing fatigue failure. While such mesoscale models can reliably predict the [...] Read more.
Prediction of fatigue failure in concrete structures remains a major challenge due to progressive material degradation. Reliable prediction, therefore, requires modeling the 3D heterogeneous microstructure of concrete to explain the underlying mechanisms governing fatigue failure. While such mesoscale models can reliably predict the fatigue-induced fracture mechanisms, the identification of the associated material parameters remains a significant challenge due to the high-dimensional parameter space introduced by the model. The key challenge addressed in this study is to capture microcrack initiation and coalescence under fatigue loading, using a model capable of representing fracture process: crack initiation, crack propagation, and final failure. Firstly, concrete domain is discretized into Voronoi cells, enabling explicit representation of aggregates and mortar by randomly assigning cohesive links connecting Voronoi cells as aggregates and mortar. After this, mortar links are modeled as coupled damage–plasticity 3D Timoshenko beam elements with nonlinear kinematic hardening and isotropic softening introduced using embedded discontinuity formulation, enabling fracture Modes I–III, whereas aggregate links are modeled as elastic 3D Timoshenko beam elements. The model efficiency is additionally reinforced by using surrogate model approach, with corresponding material parameter identification carried out by multi-objective Bayesian optimization framework to reproduce experimental results. The performance of the proposed model is illustrated by reproducing experimental results obtained from concrete cube compression test and three-point bending test under low-cycle fatigue loading, where the errors between experimental and numerical results are reduced by 82% (stress) and 88% (energy) for the cube test and by 86% (force) and 93% (energy) for the bending test, relative to the initial dataset error. Full article
(This article belongs to the Section Computational Engineering)
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13 pages, 2355 KB  
Article
Structural Damage Identification with Machine Learning Based Bayesian Model Selection for High-Dimensional Systems
by Kunyang Wang and Yukihide Kajita
Buildings 2025, 15(24), 4456; https://doi.org/10.3390/buildings15244456 - 10 Dec 2025
Viewed by 507
Abstract
Identifying structural damage in high-dimensional systems remains a major challenge due to the curse of dimensionality and the inherent sparsity of real-world damage scenarios. Traditional Bayesian or optimization-based approaches often become computationally intractable when applied to structures with a large number of uncertain [...] Read more.
Identifying structural damage in high-dimensional systems remains a major challenge due to the curse of dimensionality and the inherent sparsity of real-world damage scenarios. Traditional Bayesian or optimization-based approaches often become computationally intractable when applied to structures with a large number of uncertain parameters, where only a few members are actually damaged. To address this problem, this study proposes a Machine Learning and Widely Applicable Information Criterion (WAIC) based Bayesian framework for efficient and accurate damage identification in high-dimensional systems. In the proposed approach, an ML is first trained using simulated modal responses under randomly generated damage patterns. The ML predicts the most likely damaged members by measured responses, effectively reducing the high-dimensional search space to a small subset of candidates. Subsequently, a WAIC is employed to estimate the model combined by these candidates, while automatically selecting the optimal damage model. By combining the localization capability of ML with the uncertainty quantification of Bayesian inference, the proposed method achieves high identification accuracy with significantly reduced computational cost of model selection. Numerical experiments on a high-dimensional truss system demonstrate that the method can accurately locate and quantify multiple damages even under noise contamination. The results confirm that the hybrid framework effectively mitigates the curse of dimensionality and provides a robust solution for structural damage identification in large-scale structural systems. Full article
(This article belongs to the Section Building Structures)
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24 pages, 5260 KB  
Article
Research on Parameter Influence of Offshore Wind Turbines Based on Measured Data Analysis
by Renfei Kuang, Jinhai Zhao, Tuo Zhang and Chengyang Li
J. Mar. Sci. Eng. 2025, 13(4), 629; https://doi.org/10.3390/jmse13040629 - 21 Mar 2025
Cited by 1 | Viewed by 1124
Abstract
Offshore wind turbines are prone to structural damage over time due to environmental factors, which increases operational costs and the risk of accidents. Early detection of structural damage through monitoring systems can help reduce maintenance costs. However, under complex external conditions and varying [...] Read more.
Offshore wind turbines are prone to structural damage over time due to environmental factors, which increases operational costs and the risk of accidents. Early detection of structural damage through monitoring systems can help reduce maintenance costs. However, under complex external conditions and varying structural parameters, existing methods struggle to accurately and quickly detect damage. Understanding the factors that influence structural health is critical for effective long-term monitoring, as these factors directly affect the accuracy and timeliness of damage identification. This study comprehensively analyzed 5 MW offshore wind turbine measurement data, including constructing a digital twin model, establishing a surrogate model, and performing a sensitivity analysis. For monopile-based turbines, sensors in x and y directions were installed at four heights on the pile foundation and tower. Via Bayesian optimization, the finite element model’s structural parameters were updated to align its modal parameters with sensor data analysis results. The update efficiencies of different objective functions and the impacts of neural network hyperparameters on the surrogate model were examined. The sensitivity of the turbine’s structural parameters to modal parameters was studied. The results showed that the modal flexibility matrix is more effective in iteration. A 128-neuron, double-hidden-layer neural network balanced computational efficiency and accuracy well in the surrogate model for modal analysis. Flange damage and soil degradation near the pile mainly impacted the turbine’s health. Full article
(This article belongs to the Section Coastal Engineering)
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36 pages, 9604 KB  
Article
A Comparative Study of Single-Chain and Multi-Chain MCMC Algorithms for Bayesian Model Updating-Based Structural Damage Detection
by Luling Liu, Hui Chen, Song Wang and Jice Zeng
Appl. Sci. 2024, 14(18), 8514; https://doi.org/10.3390/app14188514 - 21 Sep 2024
Cited by 7 | Viewed by 2653
Abstract
Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a [...] Read more.
Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge. Full article
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27 pages, 6473 KB  
Article
Bayesian-Based Hyperparameter Optimization of 1D-CNN for Structural Anomaly Detection
by Xiaofei Li, Hainan Guo, Langxing Xu and Zezheng Xing
Sensors 2023, 23(11), 5058; https://doi.org/10.3390/s23115058 - 25 May 2023
Cited by 25 | Viewed by 5495
Abstract
With the rapid development of sensor technology, structural health monitoring data have tended to become more massive. Deep learning has advantages when handling big data, and has therefore been widely researched for diagnosing structural anomalies. However, for the diagnosis of different structural abnormalities, [...] Read more.
With the rapid development of sensor technology, structural health monitoring data have tended to become more massive. Deep learning has advantages when handling big data, and has therefore been widely researched for diagnosing structural anomalies. However, for the diagnosis of different structural abnormalities, the model hyperparameters need to be adjusted according to different application scenarios, which is a complicated process. In this paper, a new strategy for building and optimizing 1D-CNN models is proposed that is suitable for diagnosing damage to different types of structure. This strategy involves optimizing hyperparameters with the Bayesian algorithm and improving model recognition accuracy using data fusion technology. Under the condition of sparse sensor measurement points, the entire structure is monitored, and the high-precision diagnosis of structural damage is performed. This method improves the applicability of the model to different structure detection scenarios, and avoids the shortcomings of traditional hyperparameter adjustment methods based on experience and subjectivity. In preliminary research on the simply supported beam test case, the efficient and accurate identification of parameter changes in small local elements was achieved. Furthermore, publicly available structural datasets were utilized to verify the robustness of the method, and a high identification accuracy rate of 99.85% was achieved. Compared with other methods described in the literature, this strategy shows significant advantages in terms of sensor occupancy rate, computational cost, and identification accuracy. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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16 pages, 11998 KB  
Article
Sound Damage Detection of Bridge Expansion Joints Using a Support Vector Data Description
by Junshi Li, Caiqian Yang and Jun Chen
Sensors 2023, 23(7), 3564; https://doi.org/10.3390/s23073564 - 29 Mar 2023
Cited by 7 | Viewed by 2866
Abstract
A novel method is proposed for the damage identification of modal bridge expansion joints (MBEJs) based on sound signals. Two modal bridge expansion joint specimens were fabricated to simulate healthy and damaged states. A microphone was used to collect the impact signals from [...] Read more.
A novel method is proposed for the damage identification of modal bridge expansion joints (MBEJs) based on sound signals. Two modal bridge expansion joint specimens were fabricated to simulate healthy and damaged states. A microphone was used to collect the impact signals from different specimens. The wavelet packet energy ratio of the sound signal was used to identify the difference in specimen state. Firstly, the wavelet packet energy ratio was used to establish the feature vectors, which were reduced dimensionality using principal component analysis. Subsequently, a support vector data description model was established to detect the difference in the signals. The identification effects of three parameter optimization methods (particle swarm optimization, genetic algorithm optimization, and Bayesian optimization) were compared. The results showed that the wavelet packet energy ratio of sound signals could effectively distinguish the state of the support bar. The support vector data description of Bayesian optimization worked best, and the proposed method could successfully detect damage to the support bar of MBEJs with an accuracy of 99%. Full article
(This article belongs to the Section Physical Sensors)
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17 pages, 4386 KB  
Article
Feature Selection and Damage Identification for Urban Railway Track Using Bayesian Globally Sparse Principal Component Analysis
by Qi Li, Yong Huang, Jiahui Chen, Xiaohui Liu, Xianghao Meng and Chao Lin
Sustainability 2023, 15(6), 5391; https://doi.org/10.3390/su15065391 - 17 Mar 2023
Cited by 5 | Viewed by 2184
Abstract
Urban railway track infrastructures often suffer from damage that affects their service performance due to a variety of factors. In this study, an unsupervised feature selection and damage identification method based on globally sparse probabilistic principal component analysis (PCA) is proposed for urban [...] Read more.
Urban railway track infrastructures often suffer from damage that affects their service performance due to a variety of factors. In this study, an unsupervised feature selection and damage identification method based on globally sparse probabilistic principal component analysis (PCA) is proposed for urban railway tracks using the monitoring data of train-induced dynamic responses. A Bayesian framework is proposed for generating principal components on a basis of vectors (original variables) with a global sparseness pattern instead of separate patterns in a traditional sparse PCA. In this framework, a variational expectation-maximization algorithm is employed to obtain the tractable calculation of the marginal likelihood function for learning all uncertain parameters of the Bayesian model. The obtained principal components are linear combinations of the very same set of important variables, making our method better interpretable than the traditional sparse PCA. We can clearly understand which original variables are most relevant for describing the data. The track damage is identified simply by discriminating the corresponding measured dynamic responses using the binary elements of the latent vector inferred from the Bayesian globally sparse PCA algorithm. The usefulness is demonstrated by successfully identifying the track bed plate crack damage through the actual train-induced dynamic responses collected from the structural health monitoring system of an urban railway track infrastructure, where the method is able to achieve F1 scores of 90% or higher for various scenarios. Full article
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24 pages, 5942 KB  
Article
Probabilistic Structural Model Updating with Modal Flexibility Using a Modified Firefly Algorithm
by Zhouquan Feng, Wenzan Wang and Jiren Zhang
Materials 2022, 15(23), 8630; https://doi.org/10.3390/ma15238630 - 3 Dec 2022
Cited by 7 | Viewed by 2088
Abstract
Structural model updating is one of the most important steps in structural health monitoring, which can achieve high-precision matching between finite element models and actual engineering structures. In this study, a Bayesian model updating method with modal flexibility was presented, where a modified [...] Read more.
Structural model updating is one of the most important steps in structural health monitoring, which can achieve high-precision matching between finite element models and actual engineering structures. In this study, a Bayesian model updating method with modal flexibility was presented, where a modified heuristic optimization algorithm named modified Nelder–Mead firefly algorithm (m-NMFA) was proposed to find the most probable values (MPV) of model parameters for the maximum a posteriori probability (MAP) estimate. The proposed m-NMFA was compared to the original firefly algorithm (FA), the genetic algorithm (GA), and the particle swarm algorithm (PSO) through the numerical illustrative examples of 18 benchmark functions and a twelve-story shear frame model. Then, a six-story shear frame model test was performed to identify the inter-story stiffness of the structure in the original and the damage states, respectively. By comparing the two, the position and extent of damage were accurately found and quantified in a probabilistic manner. In terms of optimization, the proposed m-NMFA was powerful to find the MPVs much faster and more accurately. In the incomplete measurement case, only the m-NMFA achieved target damage identification results. The proposed Bayesian model updating method has the advantages of high precision, fast convergence, and strong robustness in MPV finding and the ability of parameter uncertainty quantification. Full article
(This article belongs to the Special Issue Advances in Structural Health Monitoring for Infrastructures)
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14 pages, 708 KB  
Article
Force-Sensorless Identification and Classification of Tissue Biomechanical Parameters for Robot-Assisted Palpation
by Alejandro Gutierrez-Giles, Miguel A. Padilla-Castañeda, Luis Alvarez-Icaza and Enoch Gutierrez-Herrera
Sensors 2022, 22(22), 8670; https://doi.org/10.3390/s22228670 - 10 Nov 2022
Cited by 5 | Viewed by 3051
Abstract
The implementation of robotic systems for minimally invasive surgery and medical procedures is an active topic of research in recent years. One of the most common procedures is the palpation of soft tissues to identify their mechanical characteristics. In particular, it is very [...] Read more.
The implementation of robotic systems for minimally invasive surgery and medical procedures is an active topic of research in recent years. One of the most common procedures is the palpation of soft tissues to identify their mechanical characteristics. In particular, it is very useful to identify the tissue’s stiffness or equivalently its elasticity coefficient. However, this identification relies on the existence of a force sensor or a tactile sensor mounted at the tip of the robot, as well as on measuring the robot velocity. For some applications it would be desirable to identify the biomechanical characteristics of soft tissues without the need for a force/tactile nor velocity sensors. An estimation of such quantities can be obtained by a model-based state observer for which the inputs are only the robot joint positions and its commanded joint torques. The estimated velocities and forces can then be employed for closed-loop force control, force reflection, and mechanical parameters estimation. In this work, a closed-loop force control is proposed based on the estimated contact forces to avoid any tissue damage. Then, the information from the estimated forces and velocities is used in a least squares estimator of the mechanical parameters. Moreover, the estimated biomechanical parameters are employed in a Bayesian classifier to provide further help for the physician to make a diagnosis. We have found that a combination of the parameters of both linear and nonlinear viscoelastic models provide better classification results: 0% misclassifications against 50% when using a linear model, and 3.12% when using only a nonlinear model, for the case in which the samples have very similar mechanical properties. Full article
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21 pages, 5201 KB  
Article
Estimation and Reliability Research of Post-Earthquake Traffic Travel Time Distribution Based on Floating Car Data
by Yongyi Li, Shiqi Wang, Xiaorui Zhang and Mengxing Lv
Appl. Sci. 2022, 12(18), 9129; https://doi.org/10.3390/app12189129 - 11 Sep 2022
Cited by 4 | Viewed by 2700
Abstract
To carry out the estimation and reliability research of post-earthquake traffic travel time, which has the great influence for efficient allocation of relief materials. By analyzing the relationship among floating vehicle trajectory, target path and road network path, the intermediate parameters of converting [...] Read more.
To carry out the estimation and reliability research of post-earthquake traffic travel time, which has the great influence for efficient allocation of relief materials. By analyzing the relationship among floating vehicle trajectory, target path and road network path, the intermediate parameters of converting floating vehicle trajectory data into target path travel time were defined and improved. In addition, the road damage identification method relying on lane detection is applied for evaluating the damage of road after the earthquake through the image information. Then, Bayesian average adaptive kernel density estimation method was used to estimate the distribution of post-earthquake road travel time, and a new formula for calculating the reliability of road travel time after earthquake was proposed. According to the example simulation and analysis, the proposed post-earthquake road travel time distribution estimation and its reliability are verified. The results show that when the threshold value is determined, the travel time of the path before the earthquake is the most dependable, and with the increase in the earthquake damage index, the travel time of this road section becomes increasingly unreliable. However, after the earthquake, the peak probability density of road travel time distribution weakens, and the overall probability shifts to the direction of long time. Full article
(This article belongs to the Special Issue Seismic Performance Assessment for Structures)
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18 pages, 1816 KB  
Article
Bayesian Parameter Determination of a CT-Test Described by a Viscoplastic-Damage Model Considering the Model Error
by Ehsan Adeli, Bojana Rosić, Hermann G. Matthies, Sven Reinstädler and Dieter Dinkler
Metals 2020, 10(9), 1141; https://doi.org/10.3390/met10091141 - 24 Aug 2020
Cited by 15 | Viewed by 3391
Abstract
The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore identification of the model parameters of the system is a topic which [...] Read more.
The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the Choboche model with a damage is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data. Then the model and damage parameters are identified by applying the sequential Gauss-Markov-Kalman filter (SGMKF) approach as this method is determined as the most efficient method for time consuming finite element model updating problems among filtering and random walk approaches. The parameters identified using this Bayesian approach are compared with the true parameters in the simulation, and further, the efficiency of the identification method is discussed. The aim of this study is to observe whether the mentioned method is suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, for a real structural specimen using a limited surface displacement measurement vector gained by Digital Image Correlation (DIC) and to see how much information is indeed needed to estimate the parameters accurately even by considering the model error and whether this approach can also practically be used for health monitoring purposes before the occurrence of severe damage and collapse. Full article
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25 pages, 1680 KB  
Article
Comparison of Bayesian Methods on Parameter Identification for a Viscoplastic Model with Damage
by Ehsan Adeli, Bojana Rosić, Hermann G. Matthies, Sven Reinstädler and Dieter Dinkler
Metals 2020, 10(7), 876; https://doi.org/10.3390/met10070876 - 1 Jul 2020
Cited by 16 | Viewed by 4054
Abstract
The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which [...] Read more.
The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss-Markov-Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately. Full article
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23 pages, 478 KB  
Article
Semi-Supervised Bayesian Classification of Materials with Impact-Echo Signals
by Jorge Igual, Addisson Salazar, Gonzalo Safont and Luis Vergara
Sensors 2015, 15(5), 11528-11550; https://doi.org/10.3390/s150511528 - 19 May 2015
Cited by 30 | Viewed by 5900
Abstract
The detection and identification of internal defects in a material require the use of some technology that translates the hidden interior damages into observable signals with different signature-defect correspondences. We apply impact-echo techniques for this purpose. The materials are classified according to their [...] Read more.
The detection and identification of internal defects in a material require the use of some technology that translates the hidden interior damages into observable signals with different signature-defect correspondences. We apply impact-echo techniques for this purpose. The materials are classified according to their defective status (homogeneous, one defect or multiple defects) and kind of defect (hole or crack, passing through or not). Every specimen is impacted by a hammer, and the spectrum of the propagated wave is recorded. This spectrum is the input data to a Bayesian classifier that is based on the modeling of the conditional probabilities with a mixture of Gaussians. The parameters of the Gaussian mixtures and the class probabilities are estimated using an extended expectation-maximization algorithm. The advantage of our proposal is that it is flexible, since it obtains good results for a wide range of models even under little supervision; e.g., it obtains a harmonic average of precision and recall value of 92.38% given only a 10% supervision ratio. We test the method with real specimens made of aluminum alloy. The results show that the algorithm works very well. This technique could be applied in many industrial problems, such as the optimization of the marble cutting process. Full article
(This article belongs to the Section Physical Sensors)
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