Nonlinear structural damage detection based on cascade of Hammerstein models

Structural damages can result in nonlinear dynamical signatures that can significantly enhance their detection. An original nonlinear damage detection approach is proposed that is based on a cascade of Hammerstein models representation of the structure. This model is estimated by means of the Exponential Sine Sweep Method from only one measurement. On the basis of this estimated model, the linear and nonlinear parts of the output are estimated, and two damage indexes (DIs) are proposed. The first DI is built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI is the angle between the subspaces obtained from the nonlinear parts of two set of outputs after a principal component analysis. The sensitivity of the proposed DIs to the presence of damages as well as their robustness to noise are assessed numerically on spring-mass-damper structures and experimentally on actual composite plates with surface-mounted PZT-elements. Results demonstrate the effectiveness of the proposed method to detect a damage in nonlinear structures and in the presence of noise

A General Bayesian Framework for Ellipse-based and Hyperbola-based Damage Localisation in Anisotropic Composite Plates

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.Projet CORALI

Effects of temperature on the impedance of piezoelectric actuators used for SHM

— 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.Projet AIRCELLE (EPICE/CORALIE

Structural health monitoring of high voltage electrical switch ceramic insulators in seismic areas

High voltage electrical switches are crucial components to restart rapidly the electrical network right after an earthquake. But there currently exists no automatic procedure to check if these ceramic insulators have suffered after an earthquake, and there exists no method to recertify a given switch. To deploy a vibration-based structural health monitoring method on ceramic insulators a large shake table able to generate accelerations up to 3 g was used. The idea underlying the SHM procedure proposed here is to monitor the apparition of cracks in the ceramic insulators at their early stage through the change of the resonant frequency of the first mode of the structure and the non-linearity that they generate in its dynamic response. The Exponential Sine Sweep Method is used to estimate a nonlinear model of the structure under test from only one dynamic measurement. A classic linear damage index (DI) based on the variation of the frequency of the first mode is compared to an original nonlinear one using the ratio of the amplitudes of the third harmonic and the fundamental frequency. Results show that both DIs increase monotonically with the number of solicitations, thus validating the use of the nonlinear DI. It is also shown that the nonlinear DI presented here seems more sensitive than the linear one

Sensor validation of a Structural Health Monitoring Process for Aircraft Nacelle

This paper details the implementation process of an embedded structural health monitoring (SHM) system enabling condition-based maintenance of aircraft nacelles. One critical issue before being able to make use of such system is to ensure the effective bonding of the chosen actuators and sensors with their host structure, especially as the latter will be exposed to harsh environments and wide operational variability. In this work, we are concerned with the composite components of the nacelle and we use piezoelectric elements as both sensors and actuators. We propose an integrated approach that allows to validate a combination “Substrate—Glue—Piezoelectric” (SGP) and thus provides criteria to choose and size these assemblies. This validation scheme is based on the observation of the variations of the static capacity of the piezoelectric element after enduring various temperature and stress conditions when bonded to its host structure. Based on those SGP combinations, an active SHM strategy interrogating the structure by means of elastic wave propagation is currently being developed and preliminary results on samples representative of the nacelle are presented and discussed.Projet AIRCELLE (EPICE/CORALIE

Peaks Over Threshold Method for Structural Health Monitoring Detector Design

Structural Health Monitoring (SHM) system offers new approaches to interrogate the integrity of structures. The most critical step of such systems is the damage detection step since it is the first and because performances of the following steps (damage localization, severity estimation…) depend on it. Care has thus to be taken when designing the detector. The objective of this communication is to discuss issues related to the design of a detector for the structural health monitoring of composite structures. The structure under monitoring is a substructure of an aircraft nacelle. In the absence of damage, the detector principle is to statistically characterize the healthy behavior of the structure. This characterization is based on the availability of a decision statistics synthesized from a damage index. Airline business models rely on Probability of False Alarms (Pfa) as main performance criterion. In general, the requirement on Pfa is 10E-9 which is very small. To determine the decision threshold, the approach we consider, consists to model the tail of the decision statistics using the Peaks Over Threshold method extracted from the extreme value theory (EVT). This method has been applied for different configuration of learning sample and probability of false alarm. This approach of tail distribution estimation is interesting since it is not necessary to know the distribution of the decision statistic to develop a detector. However, its main drawback is that it is necessary to have very large databases to accurately estimate decision thresholds to then decide the presence or absence of damage

Contrôle santé des structures basé sur la signature dynamique non-linéaire de dommages

La mise en place de procédures de contrôle automatisé de l’endommagement de structures issues de l’aéronautique ou du génie civil constitue une thématique émergente nommée « Contrôle de la santé des structures » (SHM : « Structural Health Monitoring »). Le déploiement de ces procédures laisse présager d’importantes améliorations en termes de sécurité ainsi qu’une réduction substantielle des couts de maintenance. Les procédures de SHM sont habituellement divisées séquentiellement en quatre étapes : détection, localisation, classification, puis quantification de l’endommagement. Les dommages apparaissant dans ces structures sont à l’origine de non-linéarités dans la réponse dynamique de ces structures qui ne sont pour l’instant pas ou peu utilisées à des fins de SHM. Nous verrons ainsi dans ce séminaire que, s’il est possible d’estimer efficacement la signature non-linéaire des dommages, cette information s’avère être un indicateur extrêmement sensible pour la surveillance des dommages. Du point de vue mathématique les travaux présentés ici s’appuient sur une classe de modèles non-linéaires par bloc prometteuse : les modèles de Hammerstein en parallèle. L’intérêt de cette classe de modèles est qu’elle est à la fois simple à estimer et représentative d’un large panel de structures endommagées. Nous verrons ainsi, qu’à partir d’une représentation non-linéaire plus riche tirée de ces modèles, des algorithmes de SHMs liés aux phases de détection, de classification, et de quantification des dommages peuvent être développés. Ces algorithmes seront illustrés dans des contextes « aéronautique » ou « génie civil » sur des données numériques et expérimentales

From nonlinear system identification to structural health monitoring

The process of implementing a damage monitoring strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM) and implies a sensor network that monitors the behavior of the structure on-line. A SHM process potentially allows for an optimal use of the monitored structure, a minimized downtime, and the avoidance of catastrophic failures. The SHM process classically relies on four sequential steps that are damage detection, localization, classification, and quantification. The key idea underlying this seminary is that structural damages may result in nonlinear dynamical signatures that are not yet used in SHM despite the fact that they can significantly enhance their monitoring. We thus propose to monitor these structural damages by identifying their nonlinear signature on the basis of a cascade of Hammerstein models representation of the structure. This model is here estimated at very low computational cost by means of the Exponential Sine Sweep Method. It will be shown that on the basis of this richer dynamical representation of the structure, SHM algorithms dedicated to damage detection, classification and quantification can be derived. This will be illustrated in the aeronautic and civil engineering contexts and using experimental as well as numerical data

Damage type classification based on structures nonlinear dynamical signature

Structural damages result in nonlinear dynamical signatures that significantly help for their monitoring. A damage type classification approach is proposed here that is based on a parallel Hammerstein models representation of the structure estimated by means of the Exponential Sine Sweep Method. This estimation method has been here extended to take into account for input signal amplitude which was not the case before. On the basis of these estimated models, three amplitude dependent damage indexes are built: one that monitors the shift of the resonance frequency of the structure, another the ratio of nonlinear versus linear energy in the output signal, and a last one the ratio of the energy coming from odd nonlinearities to the energy coming from even nonlinearities in the output signal. The slopes of these amplitude-dependent DIs are then used as coordinates to place the damaged structure under study within a three-dimensional space. A single mass-spring-damper system is considered to illustrate the ability of this space to classify different types of damage. Four types of damage with different severities are simulated through different spring nonlinearities: bilinear stiffness, dead zone, saturation, and Coulomb friction. For all severities, the four types of damage are extremely well separated within the proposed three-dimensional space, thus highlighting its high potential for classification purposes

Optimal Sensors Placement to Enhance Damage Detection in Composite Plates

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.Projet AIRCELLE (EPICE/CORALIE