Marc Rébillat

A general Bayesian framework for ellipse-based and hyperbola-based damage localization in anisotropic composite plates

This article focuses on Bayesian Lamb wave-based damage localization in structural health monitoring of anisotropic composite materials. A Bayesian framework is applied to take account of uncertainties from experimental time-of-flight measurements and angle-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 (ellipse-based) and time-difference-of-arrival (hyperbola-based) Bayesian damage localization algorithms. This way, the damage location and the group velocity profile are estimated jointly and a priori information is taken into consideration. The proposed algorithm is general as it allows us to take into account 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.

Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties

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.

On the variation of interaural time differences with frequency

Interaural time difference (ITD) is a major cue to sound localization in humans and animals. For a given subject and position in space, ITD depends on frequency. This variation is analyzed here using a head related transfer functions (HRTFs) database collected from the literature and comprising human HRTFs from 130 subjects and animal HRTFs from six specimens of different species. For humans, the ITD is found to vary with frequency in a way that shows consistent differences with respect to a spherical head model. Maximal ITD values were found to be about 800 μs in low frequencies and 600 μs in high frequencies. The ITD variation with frequency (up to 200 μs for some positions) occurs within the frequency range where ITD is used to judge the lateral position of a sound source. In addition, ITD varies substantially within the bandwidth of a single auditory filter, leading to systematic differences between envelope and fine-structure ITDs. Because the frequency-dependent pattern of ITD does not display spherical symmetries, it potentially provides cues to elevation and resolves front/back confusion. The fact that the relation between position and ITDs strongly depends on the sounds spectrum in turn suggests that humans and animals make use of this relationship for the localization of sounds.

Estimation of the low-frequency components of the head-related transfer functions of animals from photographs

Reliable animal head-related transfer function (HRTF) estimation procedures are needed for several practical applications, for example, to investigate the neuronal mechanisms of sound localization using virtual acoustic spaces or to have a quantitative description of the different localization cues available to a given animal species. Here, two established techniques are combined to estimate an animals HRTF from photographs by taking into account as much morphological detail as possible. The first step of the method consists in building a three-dimensional-model of the animal from pictures taken with a standard camera. The HRTFs are then estimated by means of a rapid boundary-element-method implementation. This combined method is validated on a taxidermist model of a cat by comparing binaural and monaural localization cues extracted from estimated and measured HRTFs. It is shown that it provides a reliable way to estimate low-frequency HRTF, which is difficult to obtain with standard acoustical measurements procedures because of reflections.

A data-driven temperature compensation approach for Structural Health Monitoring using Lamb waves

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 16 ° C to 85 ° C . 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.

A spherical cross-channel algorithm for binaural sound localization

This paper proposes a sound localization algorithm inspired by a cross-channel algorithm first studied by MacDonald et. al in 2008. The original algorithm assumes that the Head Related Transfer Functions (HRTFs) of the robotic head under study are precisely known, which is rarely the case in practice. Following the idea that any head is more or less spherical, the above assumption is relaxed by using HRTFs computed using a simple spherical head model with the same head radius as the robot head. In order to evaluate the proposed approach in realistic noisy conditions, an isotropic noise field is also computed and a precise definition of the Signal to Noise Ratio (SNR) in a binaural context is outlined. All these theoretical developments are finally assessed with simulated and experimental signals. Despite its simplicity, the proposed approach appears to be robust to noise and to provide reliable sound localization estimations in the frontal azimuthal plane.

Peaks Over Threshold–based detector design for structural health monitoring: Application to aerospace structures

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 10−4 and 10−9) 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.

On-board Decision Making Platform for Structural Health Monitoring

The ability to monitor the health of complex structures such as aeronautic or civil engineering structures in real time is becoming increasingly important. This process is referred to as structural health monitoring (SHM) and relies on onboard platforms comprising sensors, computational units, communication resources, and sometimes actuators. Many of such platforms have been developed within the last years but there is still a lack of structuration and knowledge exchange regarding the software and hardware architectures of such platforms. The aim of the present paper is to introduce an open hardware and open software platform dedicated to SHM within the fields of aeronautics and civil engineering. The platform presented here will be made available in an open hardware and open source framework to allow SHM researchers to run concurrent detection, localization, classification or quantification algorithms using simple interpreted languages such as Python.

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. doi: 10.12783/SHM2015/297