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http://hdl.handle.net/10985/10522
Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties
REBILLAT, Marc; EGE, Kerem; GALLO, Maxime; ANTONI, Jérôme
Measurements on vibrating structures has been a topic of interest for decades. Vibrating structures are however generally assumed to behave linearly and in a noise-free environment, which is not the case in practice. This paper provides a methodology that allows for the autonomous estimation of nonlinearities and assessment of uncertainties by bootstrap on a given vibrating structure. Nonlinearities are estimated by means of a block-oriented nonlinear model approach based on parallel Hammerstein models and on exponential sine sweeps. Estimation uncertainties are simultaneously assessed using repetitions of the input signal (multi-sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and a practical implementation of the method are discussed using an experimental example. The experiment chosen here consists in exciting a steel plate under various boundary conditions with exponential sine sweeps and at different levels in order to assess the evolution of nonlinearities and uncertainties over a wide range of frequencies and input amplitudes.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/105222015-01-01T00:00:00ZREBILLAT, MarcEGE, KeremGALLO, MaximeANTONI, JérômeMeasurements on vibrating structures has been a topic of interest for decades. Vibrating structures are however generally assumed to behave linearly and in a noise-free environment, which is not the case in practice. This paper provides a methodology that allows for the autonomous estimation of nonlinearities and assessment of uncertainties by bootstrap on a given vibrating structure. Nonlinearities are estimated by means of a block-oriented nonlinear model approach based on parallel Hammerstein models and on exponential sine sweeps. Estimation uncertainties are simultaneously assessed using repetitions of the input signal (multi-sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and a practical implementation of the method are discussed using an experimental example. The experiment chosen here consists in exciting a steel plate under various boundary conditions with exponential sine sweeps and at different levels in order to assess the evolution of nonlinearities and uncertainties over a wide range of frequencies and input amplitudes.Detection of structural damage using the exponential sine sweep method
http://hdl.handle.net/10985/7399
Detection of structural damage using the exponential sine sweep method
REBILLAT, Marc; HAJRYA, Rafik; MECHBAL, Nazih
Structural damages can result in nonlinear dynamical responses. Thus, estimating the nonlinearities generated by damages potentially allows detecting them. In this paper, an original approach called the ES2D (Exponential Sine Sweep Damage Detection) is proposed for nonlinear damage detection. This approach is based on a damage index that reflects the ratio of the energy contained in the nonlinear part of the output versus the energy contained in its linear part. For this, we suppose that the system under study can be modeled as a cascade of Hammerstein models, made of N branches in parallel composed of an elevation to the nth power followed by a linear filter called the nth order kernel. The Exponential Sine Sweep Method (ESSM) is then used to identify the linear and nonlinear parts of the model. Exponential sine sweeps are a class of sine sweeps that allow estimating a system’s first kernels in a wide frequency band from only one measurement. The ES2D method is illustrated experimentally on two actual composite plates with surface-mounted PZT-elements: one healthy and one damaged (impact). A given propagation path between a sensor and an actuator in the system is here under investigation. Using the ESSM, the first kernels modeling this propagation path are estimated for both the damaged and undamaged states. On the basis of these estimated first Kernels, the damage index is built. Its detecting efficiency and its insensitivity to environmental noise are then assessed.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/73992013-01-01T00:00:00ZREBILLAT, MarcHAJRYA, RafikMECHBAL, NazihStructural damages can result in nonlinear dynamical responses. Thus, estimating the nonlinearities generated by damages potentially allows detecting them. In this paper, an original approach called the ES2D (Exponential Sine Sweep Damage Detection) is proposed for nonlinear damage detection. This approach is based on a damage index that reflects the ratio of the energy contained in the nonlinear part of the output versus the energy contained in its linear part. For this, we suppose that the system under study can be modeled as a cascade of Hammerstein models, made of N branches in parallel composed of an elevation to the nth power followed by a linear filter called the nth order kernel. The Exponential Sine Sweep Method (ESSM) is then used to identify the linear and nonlinear parts of the model. Exponential sine sweeps are a class of sine sweeps that allow estimating a system’s first kernels in a wide frequency band from only one measurement. The ES2D method is illustrated experimentally on two actual composite plates with surface-mounted PZT-elements: one healthy and one damaged (impact). A given propagation path between a sensor and an actuator in the system is here under investigation. Using the ESSM, the first kernels modeling this propagation path are estimated for both the damaged and undamaged states. On the basis of these estimated first Kernels, the damage index is built. Its detecting efficiency and its insensitivity to environmental noise are then assessed.Optimal Sensors Placement to Enhance Damage Detection in Composite Plates
http://hdl.handle.net/10985/8234
Optimal Sensors Placement to Enhance Damage Detection in Composite Plates
FENDZI, Claude; MOREL, Julien; REBILLAT, Marc; GUSKOV, Mikhail; MECHBAL, Nazih; COFFIGNAL, Gérard
This paper examines an important challenge in ultrasonic structural health monitoring (SHM), which is the problem of the optimal placement of sensors in order to accurately detect and localize damages. The goal of this study is to enhance damage detection through an optimal sensor placement (OSP) algorithm. The problem is formulated as a global optimization problem, where the objective function to be maximized is evaluated by a ray tracing approach, which approximately models Lamb waves propagation. A genetic algorithm (GA) is then used to solve this optimization problem. Simulations and experiments were conducted to validate the proposed method on a carbon epoxy composite plate. Results show the effectiveness and the advantages of the proposed method as a tool for OSP with reasonable computation time.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/82342014-01-01T00:00:00ZFENDZI, ClaudeMOREL, JulienREBILLAT, MarcGUSKOV, MikhailMECHBAL, NazihCOFFIGNAL, GérardThis paper examines an important challenge in ultrasonic structural health monitoring (SHM), which is the problem of the optimal placement of sensors in order to accurately detect and localize damages. The goal of this study is to enhance damage detection through an optimal sensor placement (OSP) algorithm. The problem is formulated as a global optimization problem, where the objective function to be maximized is evaluated by a ray tracing approach, which approximately models Lamb waves propagation. A genetic algorithm (GA) is then used to solve this optimization problem. Simulations and experiments were conducted to validate the proposed method on a carbon epoxy composite plate. Results show the effectiveness and the advantages of the proposed method as a tool for OSP with reasonable computation time.Effects of temperature on the impedance of piezoelectric actuators used for SHM
http://hdl.handle.net/10985/8222
Effects of temperature on the impedance of piezoelectric actuators used for SHM
BALMES, Etienne; GUSKOV, Mikhail; REBILLAT, Marc; MECHBAL, Nazih
— FEM modeling of piezoelectric patches used as actuators and sensors for SHM applications. — Test/analysis correlation of temperature effects in piezoelectric materials and glue — Numerical methods associated with the prediction of electric transfers.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/82222014-01-01T00:00:00ZBALMES, EtienneGUSKOV, MikhailREBILLAT, MarcMECHBAL, Nazih— FEM modeling of piezoelectric patches used as actuators and sensors for SHM applications. — Test/analysis correlation of temperature effects in piezoelectric materials and glue — Numerical methods associated with the prediction of electric transfers.Simultaneous Influence of Static Load and Temperature on the Electromechanical Signature of Piezoelectric Elements Bonded to Composite Aeronautic Structures
http://hdl.handle.net/10985/11274
Simultaneous Influence of Static Load and Temperature on the Electromechanical Signature of Piezoelectric Elements Bonded to Composite Aeronautic Structures
REBILLAT, Marc; GUSKOV, Mikhail; BALMES, Etienne; MECHBAL, Nazih
Electromechanical (EM) signature techniques have raised a huge interest in the structural health-monitoring community. These methods aim at assessing structural damages and sensors degradation by analyzing the EM responses of piezoelectric components bonded to aeronautic structures. These structures are subjected simultaneously to static loads and temperature variations that affect the metrics commonly used for damage detection and sensor diagnostics. However, the effects of load and temperature on these metrics have mostly been addressed separately. This paper presents experimentations conducted to investigate the simultaneous influence of static load and temperature on these metrics for two kinds of piezoelectric elements (lead zirconate titanate (PZT) and macrofiber composite (MFC)) bonded on sandwich composite materials, for the full range of real-life conditions encountered in aeronautics. Results obtained indicate that both factors affect the metrics in a coupled manner in particular due to the variations of the mechanical properties of the bonding layer when crossing its glass transition temperature. Furthermore, both piezoelectric elements globally behave similarly when subjected to temperature variations and static loads. Simultaneous accounting of both temperature and static load is thus needed in practice in order to design reliable structural health-monitoring systems based on these metrics.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/112742016-01-01T00:00:00ZREBILLAT, MarcGUSKOV, MikhailBALMES, EtienneMECHBAL, NazihElectromechanical (EM) signature techniques have raised a huge interest in the structural health-monitoring community. These methods aim at assessing structural damages and sensors degradation by analyzing the EM responses of piezoelectric components bonded to aeronautic structures. These structures are subjected simultaneously to static loads and temperature variations that affect the metrics commonly used for damage detection and sensor diagnostics. However, the effects of load and temperature on these metrics have mostly been addressed separately. This paper presents experimentations conducted to investigate the simultaneous influence of static load and temperature on these metrics for two kinds of piezoelectric elements (lead zirconate titanate (PZT) and macrofiber composite (MFC)) bonded on sandwich composite materials, for the full range of real-life conditions encountered in aeronautics. Results obtained indicate that both factors affect the metrics in a coupled manner in particular due to the variations of the mechanical properties of the bonding layer when crossing its glass transition temperature. Furthermore, both piezoelectric elements globally behave similarly when subjected to temperature variations and static loads. Simultaneous accounting of both temperature and static load is thus needed in practice in order to design reliable structural health-monitoring systems based on these metrics.Probabilistic Decision Trees using SVM for Multi-class Classification
http://hdl.handle.net/10985/7401
Probabilistic Decision Trees using SVM for Multi-class Classification
URIBE, Juan Sebastian; MECHBAL, Nazih; REBILLAT, Marc; BOUAMAMA, Karima; PENGOV, Marco
In the automotive repairing backdrop, retrieving from previously solved incident the database features that could support and speed up the diagnostic is of great usefulness. This decision helping process should give a fixed number of the more relevant diagnostic classified in a likelihood sense. It is a probabilistic multi-class classification problem. This paper describes an original classification technique, the Probabilistic Decision Tree (PDT) producing a posteriori probabilities in a multi-class context. It is based on a Binary Decision Tree (BDT) with Probabilistic Support Vector Machine classifier (PSVM). At each node of the tree, a bi-class SVM along with a sigmoid function are trained to give a probabilistic classification output. For each branch, the outputs of all the nodes composing the branch are combined to lead to a complete evaluation of the probability when reaching the final leaf (representing the class associated to the branch). To illustrate the effectiveness of PDTs, they are tested on benchmark datasets and results are compared with other existing approaches.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/74012013-01-01T00:00:00ZURIBE, Juan SebastianMECHBAL, NazihREBILLAT, MarcBOUAMAMA, KarimaPENGOV, MarcoIn the automotive repairing backdrop, retrieving from previously solved incident the database features that could support and speed up the diagnostic is of great usefulness. This decision helping process should give a fixed number of the more relevant diagnostic classified in a likelihood sense. It is a probabilistic multi-class classification problem. This paper describes an original classification technique, the Probabilistic Decision Tree (PDT) producing a posteriori probabilities in a multi-class context. It is based on a Binary Decision Tree (BDT) with Probabilistic Support Vector Machine classifier (PSVM). At each node of the tree, a bi-class SVM along with a sigmoid function are trained to give a probabilistic classification output. For each branch, the outputs of all the nodes composing the branch are combined to lead to a complete evaluation of the probability when reaching the final leaf (representing the class associated to the branch). To illustrate the effectiveness of PDTs, they are tested on benchmark datasets and results are compared with other existing approaches.Peaks Over Threshold–based detector design for structural health monitoring: Application to aerospace structures
http://hdl.handle.net/10985/11775
Peaks Over Threshold–based detector design for structural health monitoring: Application to aerospace structures
REBILLAT, Marc; HMAD, Ouadie; KADRI, Farid; MECHBAL, Nazih
Structural health monitoring offers new approaches to interrogate the integrity of complex structures. The structural health monitoring process classically relies on four sequential steps: damage detection, localization, classification, and quantification. The most critical step of such process is the damage detection step since it is the first one and because performances of the following steps depend on it. A common method to design such a detector consists of relying on a statistical characterization of the damage indexes available in the healthy behavior of the structure. On the basis of this information, a decision threshold can then be computed in order to achieve a desired probability of false alarm. To determine the decision threshold corresponding to such desired probability of false alarm, the approach considered here is based on a model of the tail of the damage indexes distribution built using the Peaks Over Threshold method extracted from the extreme value theory. This approach of tail distribution estimation is interesting since it is not necessary to know the whole distribution of the damage indexes to develop a detector, but only its tail. This methodology is applied here in the context of a composite aircraft nacelle (where desired probability of false alarm is typically between 1024 and 1029) for different configurations of learning sample size and probability of false alarm and is compared to a more classical one which consists of modeling the entire damage indexes distribution by means of Parzen windows. Results show that given a set of data in the healthy state, the effective probability of false alarm obtained using the Peaks Over Threshold method is closer to the desired probability of false alarm than the one obtained using the Parzen-window method, which appears to be more conservative.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/117752018-01-01T00:00:00ZREBILLAT, MarcHMAD, OuadieKADRI, FaridMECHBAL, NazihStructural health monitoring offers new approaches to interrogate the integrity of complex structures. The structural health monitoring process classically relies on four sequential steps: damage detection, localization, classification, and quantification. The most critical step of such process is the damage detection step since it is the first one and because performances of the following steps depend on it. A common method to design such a detector consists of relying on a statistical characterization of the damage indexes available in the healthy behavior of the structure. On the basis of this information, a decision threshold can then be computed in order to achieve a desired probability of false alarm. To determine the decision threshold corresponding to such desired probability of false alarm, the approach considered here is based on a model of the tail of the damage indexes distribution built using the Peaks Over Threshold method extracted from the extreme value theory. This approach of tail distribution estimation is interesting since it is not necessary to know the whole distribution of the damage indexes to develop a detector, but only its tail. This methodology is applied here in the context of a composite aircraft nacelle (where desired probability of false alarm is typically between 1024 and 1029) for different configurations of learning sample size and probability of false alarm and is compared to a more classical one which consists of modeling the entire damage indexes distribution by means of Parzen windows. Results show that given a set of data in the healthy state, the effective probability of false alarm obtained using the Peaks Over Threshold method is closer to the desired probability of false alarm than the one obtained using the Parzen-window method, which appears to be more conservative.A data-driven temperature compensation approach for Structural Health Monitoring using Lamb waves
http://hdl.handle.net/10985/11239
A data-driven temperature compensation approach for Structural Health Monitoring using Lamb waves
FENDZI, Claude; REBILLAT, Marc; MECHBAL, Nazih; GUSKOV, Mikhail; COFFIGNAL, Gérard
This paper presents a temperature compensation method for Lamb wave structural health monitoring. The proposed approach considers a representation of the piezo-sensor signal through its Hilbert transform that allows one to extract the amplitude factor and the phase shift in signals caused by temperature changes. An ordinary least square (OLS) algorithm is used to estimate these unknown parameters. After estimating these parameters at each temperature in the operating range, linear functional relationships between the temperature and the estimated parameters are derived using the least squares method. A temperature compensation model is developed based on this linear relationship that allows one to reconstruct sensor signals at any arbitrary temperature. The proposed approach is validated numerically and experimentally for an anisotropic composite plate at different temperatures ranging from Formula to Formula . A close match is found between the measured signals and the reconstructed ones. This approach is interesting as it needs only a limited set of piezo-sensor signals at different temperatures for model training and temperature compensation at any arbitrary temperature. Damage localization results after temperature compensation demonstrate its robustness and effectiveness.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/112392016-01-01T00:00:00ZFENDZI, ClaudeREBILLAT, MarcMECHBAL, NazihGUSKOV, MikhailCOFFIGNAL, GérardThis paper presents a temperature compensation method for Lamb wave structural health monitoring. The proposed approach considers a representation of the piezo-sensor signal through its Hilbert transform that allows one to extract the amplitude factor and the phase shift in signals caused by temperature changes. An ordinary least square (OLS) algorithm is used to estimate these unknown parameters. After estimating these parameters at each temperature in the operating range, linear functional relationships between the temperature and the estimated parameters are derived using the least squares method. A temperature compensation model is developed based on this linear relationship that allows one to reconstruct sensor signals at any arbitrary temperature. The proposed approach is validated numerically and experimentally for an anisotropic composite plate at different temperatures ranging from Formula to Formula . A close match is found between the measured signals and the reconstructed ones. This approach is interesting as it needs only a limited set of piezo-sensor signals at different temperatures for model training and temperature compensation at any arbitrary temperature. Damage localization results after temperature compensation demonstrate its robustness and effectiveness.Effects of temperature on the impedance of piezoelectric actuators used for SHM
http://hdl.handle.net/10985/8591
Effects of temperature on the impedance of piezoelectric actuators used for SHM
BALMES, Etienne; GUSKOV, Mikhail; REBILLAT, Marc; MECHBAL, Nazih
— FEM modeling of piezoelectric patches used as actuators and sensors for SHM applications. — Test/analysis correlation of temperature effects in piezoelectric materials and glue — Numerical methods associated with the prediction of electric transfers.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/85912014-01-01T00:00:00ZBALMES, EtienneGUSKOV, MikhailREBILLAT, MarcMECHBAL, Nazih— FEM modeling of piezoelectric patches used as actuators and sensors for SHM applications. — Test/analysis correlation of temperature effects in piezoelectric materials and glue — Numerical methods associated with the prediction of electric transfers.A General Bayesian Framework for Ellipse-based and Hyperbola-based Damage Localisation in Anisotropic Composite Plates
http://hdl.handle.net/10985/9218
A General Bayesian Framework for Ellipse-based and Hyperbola-based Damage Localisation in Anisotropic Composite Plates
FENDZI, Claude; MECHBAL, Nazih; REBILLAT, Marc; GUSKOV, Mikhail
This paper focuses on Bayesian Lamb wave-based damage localization in structural health monitoring of anisotropic composite materials. A Bayesian framework is applied to take account for uncertainties from experimental time-of-flight measurements and angular dependent group velocity within the composite material. An original parametric analytical expression of the direction dependence of group velocity is proposed and validated numerically and experimentally for anisotropic composite and sandwich plates. This expression is incorporated into time-of-arrival (ToA: ellipse-based) and time-difference-of-arrival (TDoA: hyperbola-based) Bayesian damage localization algorithms. This way, the damage location as well as the group velocity profile are estimated jointly and a priori information taken into consideration. The proposed algorithm is general as it allows to take into account for uncertainties within a Bayesian framework, and to model effects of anisotropy on group velocity. Numerical and experimental results obtained with different damage sizes or locations and for different degrees of anisotropy validate the ability of the proposed algorithm to estimate both the damage location and the group velocity profile as well as the associated confidence intervals. Results highlight the need to consider for anisotropy in order to increase localization accuracy, and to use Bayesian analysis to quantify uncertainties in damage localization.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/92182016-01-01T00:00:00ZFENDZI, ClaudeMECHBAL, NazihREBILLAT, MarcGUSKOV, MikhailThis paper focuses on Bayesian Lamb wave-based damage localization in structural health monitoring of anisotropic composite materials. A Bayesian framework is applied to take account for uncertainties from experimental time-of-flight measurements and angular dependent group velocity within the composite material. An original parametric analytical expression of the direction dependence of group velocity is proposed and validated numerically and experimentally for anisotropic composite and sandwich plates. This expression is incorporated into time-of-arrival (ToA: ellipse-based) and time-difference-of-arrival (TDoA: hyperbola-based) Bayesian damage localization algorithms. This way, the damage location as well as the group velocity profile are estimated jointly and a priori information taken into consideration. The proposed algorithm is general as it allows to take into account for uncertainties within a Bayesian framework, and to model effects of anisotropy on group velocity. Numerical and experimental results obtained with different damage sizes or locations and for different degrees of anisotropy validate the ability of the proposed algorithm to estimate both the damage location and the group velocity profile as well as the associated confidence intervals. Results highlight the need to consider for anisotropy in order to increase localization accuracy, and to use Bayesian analysis to quantify uncertainties in damage localization.