The objective of this team is the development of of robust and autonomous Structural Health Monitoring techniques by intrinsic coupling of statistics and thermo-aeroelastic modeling of mechanical structures. The emphasis of the team is the handling of very large systems such as the recent wind energy converters currently being installed in Europe, building on the expertise acquired by the team on bridges as an example of civil engineering structure, and for aircrafts and helicopters in the context of aero elastic instability monitoring. The necessity of system identification and damage detection that are robust to environmental variations and being designed to handle a very large model dimension motivates us. As examples, the explosion in the installed number of sensors and the robustness to temperature variation will be the main focus of the team. This implies new statistical and numerical technologies as well as improvements on the modeling of the underlying physical models. Many techniques and methods originate from the mechanical community and thus exhibit a very deep understanding of the underlying physics and mechanical behavior of the structure. On the other side, system identification techniques developed within the control community are more related to data modeling and take into account the underlying random nature of measurement noise. Bringing these two communities together is the objective of this joint team between Inria and IFSTTAR. It will results hopefully in methods numerically robust, statistically efficient and also mixing modeling of both the uncertainties related to the data and the associated complex physical models related to the laws of physics and finite element models.

Damage detection in civil structures has been a main focus over the last decade. Still, those techniques need to be matured to be operable and installed on structures in operation, and thus be robust to environmental nuisances. Then, damage localization, quantification and prognosis should be in that order addressed by the team. To be precise and efficient, it requires correct mixing between signal processing, statistical analysis, Finite Elements Models (FEM) updating and a yet to be available precise modeling of the environmental effects such as temperature through 3D field reconstruction.

Theoretical and practical questions are more and more complex. For example, in civil engineering, from handling hundreds of sensors automatically during some long period of time to localize and quantify damage with or without numerical models. Very large heavily instrumented structures are yet to come and they will ask for a paradigm in how we treat them from a renewed point of view. As the structures become large and complex, also the thermal and aeroelastic (among others) models become complex. Bridges and aircrafts are the main focus of our research. Opening our expertise on new applications topics such as helicopters and wind energy converters is also part of our priorities.

The main objectives of the team are first to pursue current algorithmic research activities, in order to accommodate still-to-be-developed complex physical models. More precisely, we want successively

The design and maintenance of flexible structures subject to noise and vibrations is an important topic in civil and mechanical engineering. It is an important component of comfort (cars and buildings) and contributes significantly to the safety related aspects of design and maintenance (aircrafts, aerospace vehicles and payloads, long-span bridges, high-rise towers... ). Requirements from these application areas are numerous and demanding.

Detailed physical models derived from first principles are developed as part of system design. These models involve the dynamics of vibrations, sometimes complemented by other physical aspects (fluid-structure interaction, aerodynamics, thermodynamics).

Laboratory and in-operation tests are performed on mock-up or real structures, in order to get so-called modal models, i.e. to extract the modes and damping factors (these correspond to system poles), the mode shapes (corresponding eigenvectors), and loads. These results are used for updating the design model for a better fit to data, and sometimes for certification purposes (e.g. in flight domain opening for new aircrafts, reception for large bridges).

The monitoring of structures is an important activity for the system maintenance and health assessment. This is particularly important for civil structures. Damaged structures would typically exhibit often very small changes in their stiffness due to the occurrence of cracks, loss of prestressing or post tensioning, chemical reactions, evolution of the bearing behavior and most importantly scour. A key difficulty is that such system characteristics are also sensitive to environmental conditions, such as temperature effects (for civil structures), or external loads (for aircrafts). In fact these environmental effects usually dominate the effect of damage. This is why, for very critical structures such as aircrafts, detailed active inspection of the structures is performed as part of the maintenance. Of course, whenever modal information is used to localize a damage, the localization of a damage should be expressed in terms of the physical model, not in terms of the modal model used in system identification. Consequently, the following elements are encountered and must be jointly dealt with when addressing these applications: design models from the system physics, modal models used in structural identification, and, of course, data from sensors. Corresponding characteristics are given now: Design models are Finite Element models, sometimes with tens or hundreds of thousands elements, depending on professional habits which may vary from one sector to another. These models are linear if only small vibrations are considered; still, these models can be large if medium-frequency spectrum of the load is significant. In addition, nonlinearities enter as soon as large vibrations or other physical phenomena (aerodynamics, thermodynamics, ..) are considered. Moreover stress-strain paths and therefore the response (and load) history comes into play.

Sensors can range from a handful of accelerometers or strain gauges, to thousands of them, if NEMS ( Nano Electro Mechanical Structures), MEMS (Microelectromechanical systems) or optical fiber sensors are used. Moreover, the sensor output can be a two-dimensional matrix if electro magnet (IR (infrared), SAR, shearography ...) or other imaging technologies are used.

The temperature constitutes an often dominant load because it can generate a deflection as important as that due to the self-weight of a bridge. In addition, it sometimes provokes abrupt slips of bridge spans on their bearing devices, which can generate significant transient stresses as well as a permanent deformation, thus contributing to fatigue.

But it is also well-known that the dynamic behavior of structures under monitoring can vary under the influence of several factors, including the temperature variations, because they modify the stiffness and thus the modes of vibration. As a matter of fact, depending on the boundary conditions of the structure, possibly uniform thermal variations can cause very important variations of the spectrum of the structure, up to

Unlike previously mentioned blind approaches, successful endeavours to eliminate the temperature from subspace-based damage detection algorithms prove the relevance of relying on predictive thermo-mechanical models yielding the prestress state and associated strains due to temperature variations. As part of the CONSTRUCTIF project supported by the "Action Concertée Incitative Sécurité Informatique" of the French Ministry for Education and Research, very encouraging results in this direction were obtained and published. They were substantiated by laboratory experiments of academic type on a simple beam subjected to a known uniform temperature. Considering the international pressure toward reliable methods for thermal elimination, these preliminary results pave the ground to a new SHM paradigm. Moreover, for one-dimensional problems, it was shown that real time temperature identification based on optimal control theory is possible provided the norm of the reconstructed heat flux is properly chosen. Finally, thermo-mechanical models of vibrating thin structures subject to thermal prestress, prestrain, geometric imperfection and damping have been extensively revisited. This project led by Inria involved IFSTTAR where the experiments were carried out. The project was over in July 2006. Note that thermo-mechanics of bridge piles combined with an ad hoc estimation of thermal gradients becomes of interest to practicing engineers. Thus, I4S's approach should suit advanced professional practice. Finite element analysis is also used to predict stresses and displacements of large bridges in Hong-Kong bay.

Temperature rejection is the primary focus and challenge for I4S's SHM projects in civil engineering, like SIMS project in Canada, ISMS in Danemark or SIPRIS in France.

A recent collaboration between Inria and IFSTTAR has demonstrated the efficiency of reflectometry-based methods for health monitoring of some civil engineering structures, notably external post-tensioned cables. Based on a mathematical model of electromagnetic propagation in mechanical structures, the measurement of reflected and transmitted electromagnetic waves by the monitored structures allows to detect structural failures. The interaction of such methods with those based on mechanical and thermal measurements will reinforce the multidisciplinary approach developed in our team.

We will be interested in studying linear stochastic systems, more precisely, assume at hand a sequence of observations

where

1/ identify and characterize the structure of interest. It may be possible by matching a parametric model to the observed time series

2/ decide if the measured data describe a system in a so called "reference" state (the term "reference" is used in the context of fault detection, where the reference is considered to be safe) and monitor its deviations with respect f its nominal reference state.

Both problems should be addressed differently if

1/ we consider that the allocated time to measurement is large enough, resulting in a sequence of

2/ we are interested in systems, whose dynamic is fast with respect to the sampling rate, most often asking for reaction in terms of seconds. It is, for example, the case for mission critical applications such as in-flight control or real-time security and safety assessment. Both aeronautics and transport or utilities infrastructures are concerned. In this case, fast algorithms with sample-by-sample reaction are necessary.

The monitoring of mechanical structures can not be addressed without taking into account the close environment of the considered system and their interactions. Typically, monitored structures of interest do not reside in laboratory but are considered in operational conditions, undergoing temperature, wind and humidity variations, as well as traffic, water flows and other natural or man-made loads. Those variations imply a variation of the eigenproperties of the monitored structure, which need to be separated from the damage/instability induced variations.

For example, in civil engineering, an essential problem for in-operation health monitoring of civil structures is the variation of the environment itself. Unlike laboratory experiments, civil structure modal properties change during time as temperature and humidity vary. Traffic and comparable transient events also influence the structures. Thus, structural modal properties are modified by slow low variations, as well as fast transient non stationarities. From a damage detection point of view, the former has to be detected, whereas the latter has to be neglected and should not perturb the detection. Of course, from a structural health monitoring point of view the knowledge of the true load is itself of paramount importance.

In this context, the considered perturbations will be of two kinds, either

1/ the influence of the temperature on civil structures, such as bridges or wind energy converters : as we will notice, those induced variations can be modeled by a additive component on the system stiffness matrix depending on the current temperature, as

We will then have to monitor the variations in

2/ the influence of the aeroelastic forces on aeronautical structures such as aircrafts or rockets and on flexible civil structures such as long-span bridges: we will see as well that this influence implies a modification of the classical mechanical equation (2)

where

Most of the research at Inria for a decade has been devoted to the study of subspace methods and how they handle the problems described above.

Model (2) is characterized by the following property (we formulate it for the single sensor case, to simplify notations): Let

There are numerous ways to implement those methods. This approach has seen a wide acceptance in the industry and benefits from a large background in the automatic control literature. Up to now, there was a discrepancy between the a priori efficiency of the method and some not so efficient implementations of this algorithm. In practice, for the last ten years, stabilization diagrams have been used to handle the instability and the weakness with respect to noise, as well as the poor capability of those methods to determine model orders from data. Those methods implied some engineering expertise and heavy post processing to discriminate between models and noise. This complexity has led the mechanical community to adopt preferably frequency domain methods such as Polyreference LSCF. Our focus has been on improving the numerical stability of the subspace algorithms by studying how to compute the least square solution step in this algorithm. This yields to a very efficient noise free algorithm, which has provided a renewed acceptance in the mechanical engineering community for the subspace algorithms. Now we focus on improving speed and robustness of those algorithms.

Subspace methods can also be used to test whether a given data set conforms a model: just check whether this property holds, for a given pair {data, model}. Since equality holds only asymptotically, equality must be tested against some threshold asymptotic local approach for testing between close hypotheses on long data sets — this method was introduced by Le Cam in the 70s. By using the Jacobian between pair

In oder to discriminate between damage and temperature variations, we need to monitor the variations in

This approach has been used also for flutter monitoring in Rafik Zouari's PhD thesis for handling the aeroelastic effect.

In this section, the main features for the key monitoring issues, namely identification, detection, and diagnostic, are provided, and a particular instantiation relevant for vibration monitoring is described.

It should be stressed that the foundations for identification, detection, and diagnostics, are fairly general, if not generic. Handling high order linear dynamical systems, in connection with finite elements models, which call for using subspace-based methods, is specific to vibration-based SHM. Actually, one particular feature of model-based sensor information data processing as exercised in I4S, is the combined use of black-box or semi-physical models together with physical ones. Black-box and semi-physical models are, for example, eigenstructure parameterizations of linear MIMO systems, of interest for modal analysis and vibration-based SHM. Such models are intended to be identifiable. However, due to the large model orders that need to be considered, the issue of model order selection is really a challenge. Traditional advanced techniques from statistics such as the various forms of Akaike criteria (AIC, BIC, MDL, ...) do not work at all. This gives rise to new research activities specific to handling high order models.

Our approach to monitoring assumes that a model of the monitored system is available.
This is a reasonable assumption, especially within the SHM areas.
The main feature of our monitoring method is its intrinsic ability
to the early warning of small deviations of a system with respect
to a reference (safe) behavior under usual operating
conditions, namely without any artificial excitation or other external action.
Such a normal behavior is summarized in a reference parameter vector

The behavior of the monitored continuous system is assumed to be described by
a parametric model

For reasons closely related to the vibrations monitoring applications,
we have been investigating subspace-based methods, for both the identification
and the monitoring of the eigenstructure

namely the

The (canonical) parameter vector in that case is :

where

Subspace-based methods is the generic name for linear systems identification algorithms based on either time domain measurements or output covariance matrices, in which different subspaces of Gaussian random vectors play a key role 68.

Let

be the output covariance and Hankel matrices, respectively; and:

where:

are the observability and controllability matrices, respectively.
The observation matrix

Since the actual model order is generally not known, this procedure is run with increasing model orders.

Our approach to on-board detection is based on the so-called asymptotic statistical local approach. It is worth noticing that these investigations of ours have been initially motivated by a vibration monitoring application example. It should also be stressed that, as opposite to many monitoring approaches, our method does not require repeated identification for each newly collected data sample.

For achieving the early detection of small deviations with respect to the normal behavior,
our approach generates, on the basis of the reference parameter vector

These indicators are computationally cheap, and thus can be embedded. This is of particular interest in some applications, such as flutter monitoring.

Choosing the eigenvectors of matrix

where

This property can be checked as follows. From the nominal

Matrix

Assume now that a reference ${\theta}_{0}$ and a new sample ${Y}_{1},\cdots ,{Y}_{N}$
are available.
For checking whether the data agree with

and to define the residual vector

Let

As in most fault detection approaches, the key issue is to design a residual,
which is ideally close to zero under normal operation, and has low sensitivity
to noises and other nuisance
perturbations, but high sensitivity to small deviations, before they
develop into events to be avoided (damages, faults, ...).
The originality of our approach is to:

The central limit theorem shows 62 that the residual is asymptotically Gaussian:

where the asymptotic covariance matrix

where

A further monitoring step, often called fault isolation,
consists in determining which (subsets of) components
of the parameter vector

The question: which (subsets of) components of $\theta $ have changed ?,
can be addressed
using either nuisance parameters elimination methods or a multiple hypotheses testing
approach 61.

In most SHM applications, a complex physical system, characterized by a generally
non identifiable parameter vector

The isolation methods sketched above are possible solutions to the former. Our approach to the latter diagnosis problem is basically a detection approach again, and not a (generally ill-posed) inverse problem estimation approach.

The basic idea is to note that the physical sensitivity matrix writes

It should be clear that the selection of a particular parameterization

This section introduces the infrared radiation and its link with the temperature, in the next part different measurement methods based on that principle are presented.

Infrared is an electromagnetic radiation having a wavelength between

For scientific purposes, infrared can be divided in three ranges of wavelength in which the application varies, see Table 1.

Our work is concentrated in the mid infrared spectral band. Keep in mind that Table 1 represents the ISO 20473 division scheme, in the literature boundaries between bands can move slightly.

The Planck's law, proposed by Max Planck in 1901, allows to compute the black body emission spectrum for various temperatures (and only temperatures), see Figure 2 left. The black body is a theoretical construction, it represents perfect energy emitter at a given temperature, cf. Equation (20).

With

with

By generalizing the Planck's law with the Stefan Boltzmann law (proposed first in 1879 and then in 1884 by Joseph Stefan and Ludwig Boltzmann), it is possible to address mathematically the energy spectrum of real body at each wavelength depending on the temperature, the optical condition and the real body properties, which is the base of the infrared thermography.

For example, Figure 2 right presents the energy spectrum of the atmosphere at various levels, it can be seen that the various properties of the atmosphere affect the spectrum at various wavelengths. Other important point is that the infrared solar heat flux can be approximated by a black body at 5523,15 K.

The infrared thermography is a way to measure the thermal radiation received from a medium. With that information about the electromagnetic flux, it is possible to estimate the surface temperature of the body, see section 3.5.1. Various types of detector can assure the measure of the electromagnetic radiation.

Those different detectors can take various forms and/or manufacturing process. For our research purposes, we use uncooled infrared camera using a matrix of microbolometers detectors. A microbolometer, as a lot of transducers, converts a radiation in electric current used to represent the physical quantity (here the heat flux).

This field of activity includes the use and the improvement of vision system, like in 7.

Once the acquisition process is done, it is useful to model the heat conduction inside the cartesian domain

where

An energy balance with respect to the first principle yields to the expression of the heat conduction in all point of the domain

with

To solve the system (3.6), it is necessary to express the boundary conditions of the system. With the developments presented in section 3.5.1 and the Fourier's law, it is possible, for example, to express the thermal radiation and the convection phenomenon which can occur at

Equation (3.6) is the so called Robin condition on the boundary

The systems presented in the different sections above (3.5 to 3.6) are useful to build physical models in order to represents the measured quantity. To estimate key parameters, as the conductivity, model inversion is used, the next section will introduce that principle.

Lets take any model

With

Here we want to find the solution

To do that it is important to respect the well posed condition established by Jacques Hadamard in 1902

Unfortunately those condition are rarely respected in our field of study. That is why we dont solve directly the system (25) but we minimise the quadratic coast function (26) which represents the Legendre-Gauss least square algorithm for linear problems.

where

In some cases the problem is still ill-posed and need to be regularized for example using the Tikhonov regularization. An elegant way to minimize the cost function

and find where it is equal to zero, where

Until now the inverse method proposed is valid only when the model

Equation (28) is solved iteratively at each loop

The fast development of electronic devices in modern engineering systems involves more and more connections through cables, and consequently, with an increasing number of connection failures. Wires and connectors are subject to ageing and degradation, sometimes under severe environmental conditions. In many applications, the reliability of electrical connexions is related to the quality of production or service, whereas in critical applications reliability becomes also a safety issue. It is thus important to design smart diagnosis systems able to detect connection defects in real time. This fact has motivated research projects on methods for fault diagnosis in this field. Some of these projects are based on techniques of reflectometry, which consist in injecting waves into a cable or a network and in analyzing the reflections. Depending on the injected waveforms and on the methods of analysis, various techniques of reflectometry are available. They all have the common advantage of being non destructive.

At Inria the research activities on reflectometry started within the SISYPHE EPI several years ago and now continue in the I4S EPI. Our most notable contribution in this area is a method based on the inverse scattering theory for the computation of distributed characteristic impedance along a cable from reflectometry measurements 11, 14, 67. It provides an efficient solution for the diagnosis of soft faults in electrical cables, like in the example illustrated in Figure 3.
While most reflectometry methods for fault diagnosis are based on the detection and localization of impedance discontinuity, our method yielding the spatial profile of the characteristic impedance is particularly suitable for the diagnosis of soft faults with no or weak impedance discontinuities.

Fault diagnosis for wired networks have also been studied in Inria 65, 69. The main results concern, on the one hand, simple star-shaped networks from measurements made at a single node, on the other hand, complex networks of arbitrary topological structure with complete node observations.

Though initially our studies on reflectometry were aiming at applications in electrical engineering, since the creation of the I4S team, we are also investigating applications in the field of civil engineering, by using electrical cables as sensors for monitoring changes in mechanical structures.

What follows is about some basic elements on mathematical equations of electric cables and networks, the main approach we follow in our study, and our future research directions.

A cable excited by a signal generator can be characterized by the telegrapher's equations 66

where

At the right end of the cable (corresponding to

One way for deriving the above model is to spatially discretize the cable and to characterize each small segment with 4 basic lumped parameter elements for the

A wired network is a set of cables connected at some nodes, where loads and sources can also be connected. Within each cable the current and voltage satisfy the telegrapher's equations, whereas at each node the current and voltage satisfy the Kirchhoff's laws, unless in case of connector failures.

The inverse scattering transform was developed during the 1970s-1980s for the analysis of some nonlinear partial differential equations 64. The visionary idea of applying this theory to solving the cable inverse problem goes also back to the 1980s 63. After having completed some theoretic results directly linked to practice 14, 67, we started to successfully apply the inverse scattering theory to cable soft fault diagnosis, in collaboration with GEEPS-SUPELEC 11.

To link electric cables to the inverse scattering theory, the telegrapher's equations
are transformed in a few steps to fit into a particular form studied in the inverse scattering theory. The Fourier transform is first applied to obtain a frequency domain model,
the spatial coordinate

and the frequency domain variables

with the characteristic impedance

These transformations lead to the Zakharov-Shabat equations

with

These equations have been well studied in the inverse scattering theory, for the purpose of determining partly the “potential functions”

Civil engineering:

Aeronautics:

Electrical cables and networks:

A laboratory-size prototype of the hybrid road pavement has been made within the ANR France Relance project of Domenico Vizzari with our spinoff company ECOTROPY. The objective is energy harvesting, thanks to the exploitation of solar radiation. The innovative pavement is a multilayered structure composed by a semitransparent top layer made of glass aggregates bonded together thanks to a semitransparent resin, an electrical layer containing the solar cells, a porous asphalt layer for the circulation of the calorific fluid, and finally, a base waterproof layer. The hybrid road can generate electricity, contrast the heat-island effect, exploit the harvested energy to run a heat pump for heating purposes, or facilitate road deicing during winter. Experimental data obtained through energetic tests are published in 28, showing that the prototype is able to harvest around 55.2 W through the heat-transfer fluid.

The transfer function of a linear mechanical system can be defined in terms of the quadruplet of state-space matrices (A, B, C, D) that can be identified from input and output measurements with subspace-based system identification methods. A practical algorithm for uncertainty quantification of their estimation errors and the uncertainty of the resultant parametric transfer function is missing in the context of subspace identification. In this work, explicit expressions for the covariance related to the system matrices (B, D) are developed, and applied to the covariance estimation of the resulting transfer function. This work has been done in collaboration with Brüel&Kjær. The results have been published in 19.

The interpretation of stabilization diagrams is a classical task in operational modal analysis, and has the goal to obtain the set of physical modal parameters from estimates at the different model orders of the diagram. Besides the point estimates of the modal parameters, also their confidence bounds are available with subspace identification. These uncertainties provide useful information for an automated interpretation of the stabilization diagrams. First, modes with high uncertainty are most likely non-physical modes. Second, the confidence bounds provide a natural threshold for the automated extraction of modal alignments, avoiding the requirement of a deterministic threshold regarding the allowable variation within an alignment. In this work, a strategy is presented for the automated mode extraction considering their uncertainties, based on clustering a statistical distance measures between the modes. This work has been done in collaboration with ETH Zurich and Sercel, and has been published in 52.

The quantification of statistical uncertainty in modal parameter estimates has become a standard tool, used in applications to, e.g., damage diagnosis, reliability analysis, modal tracking and model calibration. Although efficient multi-order algorithms to obtain the (co)variance of the modal parameter estimates with subspace methods have been proposed in the past, the effect of a misspecified model order on the uncertainty estimates has not been investigated. In fact, the covariance estimates may be inaccurate due to the presence of small singular values in the supposed signal space. In this work we go back to the roots of the uncertainty propagation in subspace methods and revise it to account for the case when a part of the noise space is erroneously added to the signal space. This work has been done in collaboration with ETH Zurich, and has been published in 46.

Operational wind turbines and rotating machines in general show a time periodic behavior, which does not agree with the usual assumptions of the Operational Modal Analysis (OMA) methods developed for civil engineering, where time invariant systems are considered. The existing OMA methods for rotating systems are based on pre-processing of the data to adapt to the classical identification methods. However, these methods have strong limitations and are based on strict assumptions such as the isotropy of the rotor, making difficult their application to a real case. To overcome these limitations, in this work, based on the Floquet theory, it is proposed to approximate the dynamical behavior of the periodic systems as being invariant. Thus, the classical identification methods can be safely used to retrieve the parametric signature of the periodic systems. This approach is validated on an aero-servo-elastic numerical model of a rotating 10MW wind turbine. Secondly, it is shown that the identified modes can be used for fault detection, with the detection of the rotor anisotropy using the identified mode shapes. Results have been published in 34, 36, 35, 56

The statistical subspace-based damage detection technique has shown promising theoretical and practical results for vibration-based structural health monitoring. Ideally, the reference model is assumed to be perfectly known without any uncertainty, which is not a realistic assumption in practice. Indeed, the left null space of a reference output covariance Hankel matrix is usually estimated from data to avoid model errors in the residual computation. Then, the associated uncertainties may be non-negligible, in particular when the available reference data is of limited length. In this work, it is investigated how the statistical distribution of the residual is affected when the reference null space is estimated. The asymptotic residual distribution is derived, where its refined covariance term considers also the uncertainty related to the reference null space estimate. The associated damage detection test closes a theoretical gap for real-world applications and leads to increased robustness of the method in practice. This work has been done in collaboration with BAM, Germany. The work has been published in 27.

Damage diagnosis based on global structural vibrations critically depends on the sensor layout, in particular when a small number of sensors is used for large structures under unknown excitation. This work proposes a sensor placement strategy that yields an optimized sensor layout with maximum damage detectability in selected structural components. The optimization criterion is based on the Fisher information of the design parameters of those structural components, such as material constants or cross-sectional values. It is evaluated using a finite element model, and considers the statistical uncertainties of the damage-sensitive feature. The methodology can be applied to any damage-sensitive feature whose distribution can be approximated as Gaussian. Since the Fisher information is defined component-wise, the sensor layout can be tuned to become more sensitive to damage in local structural components, such as damage hotspots, non-inspectable components, or components that are critical for the safety and serviceability of the structure. This work has been done in collaboration with University of British Columbia, Canada. The work has been published in 22.

For any structural monitoring project it is required to select relevant measurement quantities and damage-sensitive features are selected, but very few systematic approaches exist in the literature on how to select the most appropriate features. The presented work fills this gap and develops an approach based on probability of detection (POD) curves. The POD curves are generated based on a novel method for statistical damage detection tests that requires a finite element model and vibration data from the undamaged structure. The approach explicitly considers the uncertainties in the features due to unknown loads, measurement noise, and short measurement durations. Although global damage-sensitive features are considered, such as modal parameters and subspace-based residuals, the detectability is evaluated for local structural components, as well as for changes in parameters related to boundary conditions like changes in prestress or support conditions. This work has been done in collaboration with Technical University of Munich, Germany, and has been published in 48, 49 and 50.

For mechanical system structural health monitoring, a new residual generation method is proposed in this work, inspired by a recent result on subspace system identification. It improves statistical properties of the existing subspace residual, which has been naturally derived from the standard subspace system identification method. Replacing the monitored system state-space model by the Kalman filter one-step ahead predictor is the key element of the improvement in statistical properties, as originally proposed by Verhaegen and Hansson in the design of a new subspace system identification method. This work has been published in

44.

This work considers set-membership estimation for discrete-time linear parameter-varying descriptor systems. Ellipsoid bundle, a new set representation tool combining certain characteristics of ellipsoids and zonotopes, is used to design a setmembership estimation method for the considered systems. We use the L

For joint estimation of state variables and unknown parameters, adaptive observers usually assume some persistent excitation (PE) condition. In practice, the PE condition may not be satisfied, because the underlying recursive estimation problem is ill-posed. To remedy the lack of PE condition, inspired by the ridge regression, this work proposes a regularized adaptive observer with enhanced parameter adaptation gain. Like in typical ill-posed inverse problems, regularization implies an estimation bias, which can be reduced by using prior knowledge about the unknown parameters. This work has been done in collaboration with Normandie Université, and is published in 55.

To avert catastrophic failure in the structures, joints are typically designed to yield, but not fail, so that energy accumulated under cyclic loading is dissipated. Eventually, this renders the structural joints to be characteristically weaker and more vulnerable than the members. Yet, damage detection research mostly assumes damage in the members only. This work proposes a model-based predictor-corrector algorithm that uses an interacting filtering approach to efficiently estimate joint damage in the presence of input and measurement uncertainties. For the predictor model, a novel strain-displacement relationship specific to semi-rigid frames is developed to map nodal displacements to corresponding strain measurements. The proposed estimation method embeds robustness against non-stationary input (e.g. seismic excitation) in the state filter, itself. The modified state filter (robust Kalman filter) runs within an enveloping parameter filter (Particle filter) to simultaneously estimate the system states and joint damage parameters, respectively, using the response signal. This work has been done in collaboration with the Indian Institute of Technology Mandi. The work has been published in 15.

Sensor faults are inevitable during real field SHM in which sensor may malfunction or get detached from the structural surface, registering completely irrelevant information as measurement. Eventually, such erroneous information induce error in the estimation which leads to an inaccurate, sometimes divergent and impractical solution. This work deals with Bayesian filtering based structural damage detection in the presence of one or multiple (consecutive) sensor faults. The damage detection is addressed with joint state-parameter estimation while a switching filtering strategy is employed for sensor fault detection. Switching approach employs multiple possible sensor fault models which are subsequently integrated to the measurement model of the joint estimation approach. It has been demonstrated that estimation of health for structures measured with faulty sensors can actually lead to a false (positive and negative) alarm which can, however, be avoided by the employment of the proposed approach. This work has been done in collaboration with the Indian Institute of Technology Mandi. The work has been published in 16.

Tensegrities are structural mechanisms, with dedicated compression (struts/bars) and tension members (cables). Under external load, tensegrity may change its form by altering its member pre-stress, thereby affecting its global stiffness even in the absence of damage. Moreover, tensegrities can have different stiffness properties under the same structural configuration in the absence of any damage or external load, if the pre-stress levels of the members are different. However, the changes in dynamic characteristics of tensegrities are not limited to the aforementioned causes only and is also affected by ambient uncertainties. A variation in temperature may alter the dynamic characteristics of a tensegrity by influencing its material (Young's modulus, etc.) and structural (boundary conditions, structural dimensions, etc.) properties. The present work develops a vibration-based time-domain approach for tensegrity health monitoring in the presence of uncertainties due to ambient force, measurement noise, and varying temperature. An interacting filtering technique has been used, where the state variables are estimated by the Ensemble Kalman filter that resides inside the Particle filter which computes the health parameters. Furthermore, for large tensegrities that require excessive computation, only a substructure can be investigated explicitly. Yet the integration of substructures within predictor-corrector model-based SHM algorithms needs special investigation from consistency, stability, and accuracy perspectives. The need for interface measurement has been circumvented through an output injection approach. This work has been done in collaboration with the Indian Institute of Technology Mandi, and has been published in 31 and 32.

In this work the nonlinear effects induced by the presence of a transverse crack are considered to carry out vibratory monitoring and detect transverse cracks in rotating systems subject to model uncertainties. More precisely, we focus more particularly on the global complexity of the nonlinear dynamic behaviour of cracked rotors and the evolution of their harmonic components as a function of the parameters of a transverse breathing crack (its position and depth) when numerous uncertainties are considered. These random uncertainties correspond to random geometric imperfections (two disc thicknesses), random material properties (Young modulus and material density) and boundary conditions uncertainty (two bearing stiffnesses). The objective of the present work is to identify robust indicators capable of determining the presence of a crack and its status even though numerous uncertainties are present. To conduct such a study, an advanced surrogate modelling technique based on kriging and Polynomial Chaos Expansion (PCE) is proposed for the prediction of both the critical speeds and the harmonic components during passage through sub-critical resonances. The work is in collaboration with Ecole Centrale Lyon, and has been published in 23 and presented in 42 and 58.

Underplatform dampers (UPDs) are traditionally used in aircraft engines to reduce the risk of high cycle fatigue. By introducing friction in the system, vibrations at resonance are damped. However, UDPs are also the source of nonlinear behaviours making the analysis and the design of such components complex. The shape of such friction dampers has a substantial impact on the damping performances, topology optimisation is seldomly utilised-particularly for nonlinear structures. In the present work, we present a numerical approach to optimise the topology of friction dampers in order to minimise the vibration amplitude at a resonance peak. The proposed approach is based on the Moving Morphable Components framework to parametrise the damper topology, and the Efficient Global Optimisation algorithm is employed for the optimisation. The results demonstrate the relevance of such an approach for the optimisation of nonlinear vibrations in the presence of friction. New efficient damper geometries are identified in a few iterations of the algorithm, illustrating the efficiency of the approach. More generally, the different geometries are analysed and tools for clustering are proposed. The results show how topology optimisation can be employed for nonlinear vibrations to identify efficient layouts for components. The work is in collaboration with Imperial College and Rolls Royce (UK), has been published in 18 and presented at 40 and 57.

Integrally bladed disks (blisk) have been widely used in the turbo-machinery industry due to its high aerodynamic performance and structural efficiency. A friction ring damper (FRD) is usually integrated in the system to improve its low damping. However, the design of the geometry of this FRD become complex and computationally expensive due to the strong nonlinearities from friction interfaces. In this work, we propose an efficient modelling strategy based on advanced nonlinear modal analysis and Kriging surrogate models to design and optimize the geometry of a 3D FRD attached to a high fidelity full-scale blisk. The 3D ring damper is parametrised with a few key geometrical parameters. The impact of each geometric parameter and their sensitivities to nonlinear dynamic response can be efficiently assessed using Kriging meta-modelling based on a few damped nonlinear normal modes. Results demonstrate that the damping performances of ring dampers can be substantially optimized through the proposed modelling strategy whilst key insights for the design of the rings are given. It is also demonstrated that the distribution of the contact normal load on the contact interfaces has a strong influence on the damping performances and can be effectively tuned via the upper surface geometry of the ring dampers. The work is in collaboration with Imperial College and Strathclyde University (UK), and has been published in 25.

Bladed discs are a major component in turbomachinery, pushed to their limits to meet more stringent specifications to increase their performances. Structural topology optimisation allows to improve substantially the mechanical properties while drastically reducing the mass. With the coming of additive manufacturing, optimised geometry can be manufactured making this technology even more attractive. In this work, the topology of a full 3D-Finite Element Model of an academic bladed disc is optimised to improve its dynamic performances in terms of mass, stress and modal coincidences; and experimental validation is expected. First, the disc is designed to fit in the test-rig and the mechanical integrity of the 3D-printed disc is experimentally verified. Second, the topology of the blades is optimised based on a density-based approach. A methodology is proposed to perform topology optimisation for a full bladed disc and to formulate the optimisation problem. Thus, adding a static force at the blade tip forces a better material distribution over the domain and increases the blade stiffness. To minimise the number of coincidences, a numerical strategy based on iterative topology optimisation simulations is proposed to identify the correct set of frequential constraints. The work is in collaboration with Imperial College and is published in 33.

Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of microsized structures. The novelty of this work is the use of the Second Strain Gradient (SSG) theory to explore the mechanism of a micro-sized 2D beam grid. The strong formulas of continuum model including governing equations and boundary conditions are derived by using the Hamilton principle. Then, a valuable long-range Lattice Spring Model (LSM) is elaborated, providing a reasonable explanation for the model based on SSG theory. The dynamic continuum equations from LSM are computed through the Fourier series transform approach. Finally, the dynamic properties of 2D beam grid are analyzed within the Wave Finite Element Method (WFEM) framework. The band structure and slowness surfaces, confined to the irreducible first Brillouin zone, are studied in frequency spectrum. The energy flow vector fields and wave beaming effects are discussed through SSG theory and Classical Theory (CT) of elasticity. The results show that the proposed approach is of significant potential for investigating the 2D wave propagation characteristics of complex micro-sized periodic structures. The work is in collaboration with Ecole Centrale Lyon, and has been published in 30 and 54.

Surrogate models are data-based approximations of computationally expensive simulations that enable efficient exploration of the model’s design space and informed decision making in many physical domains. The usage of surrogate models in the vibroacoustic domain, however, is challenging due to the non-smooth, complex behavior of wave phenomena. This work investigates four machine learning (ML) approaches in the modelling of surrogates of sound transmission loss (STL). Feature importance and feature engineering are used to improve the models’ accuracy while increasing their interpretability and physical consistency. The transfer of the proposed techniques to other problems in the vibroacoustic domain and possible limitations of the models are discussed. Experiments show that neural network surrogates with physics-guided features have better accuracy than other ML models across different STL models. Furthermore, sensitivity analysis methods are used to assess how physically coherent the analyzed surrogates are. The work is in collaboration with Ecole Centrale Lyon and has been published in 17 and 38.

Contrary to flows in small intracranial vessels, many blood flow configurations such as those found in aortic vessels and aneurysms involve larger Reynolds numbers and, therefore, transitional or turbulent conditions. Dealing with such systems require both robust and efficient numerical methods. We assess here the performance of a lattice Boltzmann solver with full Hermite expansion of the equilibrium and central Hermite moments collision operator at higher Reynolds numbers, especially for under-resolved simulations. To that end the food and drug administration’s benchmark nozzle is considered at three different Reynolds numbers covering all regimes: 1) laminar at a Reynolds number of 500, 2) transitional at a Reynolds number of 3500, and 3) low-level turbulence at a Reynolds number of 6500. The lattice Boltzmann results are compared with previously published inter-laboratory experimental data obtained by particle image velocimetry. Our results show good agreement with the experimental measurements throughout the nozzle, demonstrating the good performance of the solver even in under-resolved simulations. In this manner, fast but sufficiently accurate numerical predictions can be achieved for flow configurations of practical interest regarding medical applications. The work is in collaboration with University of Magdeburg (Germany) and ETH Zurich (Switzerland), and has been published in 20.

DIARITsup is a chain of various softwares following the concept of "system of systems". It interconnects hardware and software layers dedicated to in-situ monitoring of structures or critical components. It embeds data assimilation capabilities combined with specific Physical or Statistical models like inverse thermal and/or mechanical ones up to the predictive ones. It aims at extracting and providing key parameters of interest for decision making tools. Its framework natively integrates data collection from local sources but also from external systems. DIARITsup is a milestone in our roadmap for SHM Digital Twins research framework. Furthermore, it intends providing some useful information for maintenance operations not only for surveyed targets but also for deployed sensors. The work has been published in 59.

Similarly to other industrial areas, there is a strong interest for the use of bonded FRP (Fiber Reinforced Polymers) repair or reinforcement for steel structures in the case of offshore applications. However, the reliability of the adhesively bonded (FRP) shall stand as high as steel renewal, this requires additional developments, in particular, a complete understanding of the repair mechanical strength which depends on material and interfacial properties. Fracture mechanics is an interesting approach to assess the risk to undergo interlaminar fracture or steel to adhesive interfacial disbonding failure. This work proposes crack front monitoring by a distributed optical fiber as an alternative to the standard techniques. Firstly, the issues related to the use of continuous optical fiber are raised (insertion, precision resolution, measurement noise, exploitation methodologies). Then, experimental investigations on ENF and DCB tests are presented and analyzed using the proposed methodology to monitor crack propagation using the optical fiber strain measurement. The results show that an optical fiber bonded on the surface of the sample can be used to measure and follow the crack propagation during the test which simplifies and adds precision to the standardize critical toughness computation method. The work is in collaboration with Bureau Veritas, and has been published in 24 and 53.

The durability of the bonded Distributed Optical Fiber Sensor (DOFS) instrumentation is investigated to assess possible alteration of its performance over aging, which would raise questions about the validity of strain measurements in the long term. In this work, steel rebars were equipped with bonded optical fibers. Half-length of the instrumented rebars was subjected to hydrothermal ageing by immersion in an alkaline solution, while the remaining length was exposed to standard laboratory conditions. After exposure, the rebars were tested in tension and the DOFS strain profiles were simultaneously measured. These strain profiles were then compared to reference measurements performed before ageing, providing insights on the influence of the ageing conditions on the response of the DOFS. This work is in collaboration with Cerema and Andra, and has been published in 39.

To prevent damage during installation and monitoring in harsh environments, the optical fiber or cable used for distributed strain measurements are always surrounded by one or several stacks of coatings made of different materials. As consequence, a mechanical strain transfer occurs. This means that a strain lag exists between the strain in the core of the optical and the one at outer of the optical fiber/cable that is sought to be measured. The strain transfer occurs on small distance (typically few centimeters). As consequence, it affects only the strain profiles measured by high-resolution distributed strain sensing systems such as the one based on the measurement of the Rayleigh back-scattering by OFDR (Optical Frequency Domain Reflectomer). In the presence of high strain gradients such as those induced by the presence of a singularity (crack) or by a particular geometry or heterogeneous assembly of different materials, the strain transfer can lead to misinterpretation of the high-resolution strain distributed measurements. A general solution describing the strain transfer for any arbitrary strain distribution is introduced in this work. This work has been published in 37.

Digital image correlation techniques are well known for motion extraction from video images. Following a two-stage approach, the pixel-level displacement is first estimated by maximizing the cross-correlation between two images, then the estimation is refined in the vicinity of the cross-correlation peak. Among existing subpixel refinement methods, quadratic surface fitting (QSF) provides good performances in terms of accuracy and computational burden. It estimates subpixel displacement by interpolating cross-correlation values with a quadratic surface. By means of counterexamples, it is shown in this work that, contrary to a widespread intuition, the quadratic surface fitted to the pixel-level cross-correlation values in the neighborhood of the cross-correlation peak does not always have a maximum. The main contribution then consists in establishing the mathematical conditions ensuring the existence of a maximum of this fitted quadratic surface, based on a rigorous analysis. Algorithm modifications for handling the failure cases of the QSF method are also proposed, in order to consolidate it for subpixel motion extraction. This work has been published in 29.

Transportation is undergoing a radical transformation toward a novel way of thinking about road pavement: a sustainable, multifunctional infrastructure able to satisfy mobility needs, ensuring high safety standards, low carbon impact, automated detection through smart sensors, and resilience against natural and anthropogenic hazards. In this scenario, the road could also play a role for energy harvesting, thanks to the exploitation of solar radiation. The latter can be directly converted into electricity by solar cells placed under a semitransparent layer, or it can be harvested through a calorific flowing fluid. The aim of this work is to introduce the concept of “hybrid road,” which is able to exploit both approaches. The innovative pavement is a multilayered structure composed by a semitransparent top layer made of glass aggregates bonded together thanks to a semitransparent resin, an electrical layer containing the solar cells, a porous asphalt layer for the circulation of the calorific fluid, and finally, a base waterproof layer. The hybrid road can generate electricity, contrast the heat-island effect, exploit the harvested energy to run a heat pump for heating purposes, or facilitate road deicing during winter. The present work details experimental data obtained through energetic tests performed with a laboratory-size prototype of the hybrid road. The results show that the prototype is able to harvest around 55.2 W through the heat-transfer fluid. Furthermore, the heat exchange between water and asphalt has a cooling effect on the entire prototype. This work has been published in 28.

Technological progress in uncooled infrared focal plane array sensors has contributed significantly to enlarge the scope of applications of such sensing technique in many domains: Leisure, Manufacturing, Process Survey, Building insulation diagnostic, Civil Engineering, Road works, etc. Different outdoor situations and objects of interest monitored by an in-house designed measurement architecture are presented. Designed instrumentation architectures and measurements correction from varying environmental conditions and geometrical considerations are discussed. A first step toward joint estimation of emissivity and temperature is introduced for outdoor applications. Then moving object detection by an AI approach applied on thermal image sequences is also presented and discussed. This work has been published in 45.

This work presents an ultra-flexible piezoelectric air flow energy harvester capable of powering a wireless sensor. The method to easily adapt the aero-electric generator to the wind is presented. In the wind tunnel, different configurations have been tested to determine the best one for energy harvesting at low wind speed. In particular, the galloping configuration, with the addition of a bluff body at the free end of the cantilever which allows to improve the performance of the micro-generator by coupling the vibrations induced by the vortices and the galloping phenomena. The effects of mechanical and electrical coupling of several generators on the performance of energy harvesting are presented. The harvested energy was then used to operate a wireless sensor. This work has been in collaboration with IETR, and has been published in 21.

The main strategic issue is the maintenance in operational condition of the Hot Box Detectors (DBC). The removal of the DBC from the track is part of Tech4Rail’s ambition: reducing equipment to the track. The innovation aimed at in this project is to study and develop a measurement solution to be deployed at the edge of a lane out of danger zone and independent of track equipment. Among the scientific obstacles identified are the following three:

A proof of concept study aims at combining real site monitoring solutions with adjoint state FE thermal model approach to predict optimal heating required to preserve surface from icing in winter conditions. Furthermore, we introduced in our prediction model connection with in-line weather forecast provided by Meteo France Geoservice at different time horizons and spatial scales. Total amount: 124 k€.

The maintenance of offshore steel structure is a great challenge. Vessels and mobile offshore units can be maintained and repaired onshore in shipyards but, fixed units, such as platforms or FPSO (Floating Production, Storage and Offloading) structures, do not come back in dry dock and shall be maintained at sea. Mostly willing in harsh offshore environment (like tropical areas), these structures are prone to the corrosion due to high temperature and high humidity conditions. To repair them, the development of new technologies based on bonding processes are interesting alternatives to the common crop and renew repair technics. In the JIP Strength Bond Offshore project launched by Bureau Veritas Marine and Offshore (BV) in March 2019 with the partners Total, Petrobras, Naval Group, Siemens, Infra-core and Coldpad, a composite patch is developed. The project aims to achieve the following main objectives:

In this project involving the laboratories UGE/MAST/SMC and UGE/COSYS/SII-I4S, the PhD student (Quentin Sourisseau) studied new approaches for the design assessment of bonded reinforcements on steel structures. These approaches were based on the use of innovative monitoring systems during fracture mechanics standardized tests (DCB for mode I loading, ENF for mode II and MMB for mixed mode) for the characterization to feed numerical design tools based on cohesive zone modelling for strength analysis. The Digital Image Correlation (DIC) was used to obtained directly the cohesive laws using the J-integral evaluation while the critical toughness was calculated from the measurement of the crack length obtained with Distributed Fiber Optic Sensors (DOFS). These parameters, the cohesive laws and the critical toughness were integrated in different modelling strategies based on finite element method. The developed methodologies were then applied to real-scale samples in order to verify their predictive capacities. Experimental results were compared to numerical predictions and to an alternative approach from the literature relying on the use of a coupled stress-energy criteria. It was conclude that the approach based of the cohesive zone modelling gave the most accurate results in the prediction in terms of mechanical behavior (strain and stress) and in terms of failure load.

Date of Phd thesis defense: 21/10/2022

With the goal of providing a complete SHM system for vibration monitoring with their high-end sensors, we have transferred modal analysis and damage detection algorithms in a technology transfer in two contracts to Sercel, involving technical development and support (2020-2022). Amount for I4S: 15k€. Besides the transfer, an ANR France Relance project with Sercel has started in 2022. Furthermore, several meetings with Sercel have happened to define joint future work, with the objective to launch a "contrat cadre" for research on SHM applications.

This mobility project with Technical University of Munich (TUM) for mutual research stays in Bavaria and France (2022–2023) is funded by the Bavarian Ministry of Science and French Ministry of Foreign Affairs, with the objective to initiate research cooperation. In this project, the goal is to develop reliability assessment strategies for SHM and NDT methods, and to aim at European fundings.

The project UNYFI (2022 – 2023) has been funded by the Royal Society of Edinburgh (RSE) between Strathclyde University and the I4S team to engage an international collaboration and initiate a research project to develop a European network and aim for European fundings.

The joint lab ASTI between Inria, University Gustave Eiffel and CNR has been approved and the letters of intent have been signed by all partners. The kick off meeting of this collaborating tri-party research lab has been postponed due to COVID.

E. Denimal collaborates with Imperial College London on the topic of structural optimisation for nonlinear vibrations. She is a visiting researcher in the Dynamics group, has co-supervied and is currently co-supervising Msc students:

Internal fundings have been secured to perform 3D printing and experimental validation of numerical works. Applications for larger calls and for the creation of an associate team are in progress.

L. Mevel is directing the thesis of Neha Aswal with S. Sen at IIT Mandi. The subject is the structural health monitoring of tensegrity structures.

C. Droz collaborates with Ecole Centrale de Lyon (France) and Compredict (Germany), through the co-supervision of a PhD student on the topic of multi-objective optimisation and digital twin for the design of lightweight transmissions.

Collaboration with IFPEN leading to the thesis of A. Cadoret on applying OMA techniques on wind turbines.

With CEA-LIST and Alstom-Rail, this project (until June 2022) focuses on NDT ultrasonic testing methods for rails. The goal is to deploy several complete rail-sensors in real railway application test benches; another aspect consists in transferring the common knowledge to the final customer Alstom. A daughter board for high frequency ultrasonic emission/reception has been successfully developed and licensed in three industrial transfers.

This governmental project aims at testing new algorithms in the CASC platform for detecting and localizing wire breaks in cables of suspension bridges by means of acoustic waves time difference of arrival (TDOA), with the objective to provide a better "time of arrival" time-stamping (by means of the maximmum of likelihood for instance). Another objective is the implementation of a good time-synchronization in wireless sensors while keeping the GPS-energy lower as possible. This was done in the context of the PhD of D. Pallier. A demonstration of acoustic sensors for bridge cable monitoring has been set up, and works for qualification carried out. The project has been prolonged until 2023.

Abstract: The six main objectives of the MINERVE project are: - Develop design and construction methods and tools using effective BIM approaches for each business - Anticipate and optimize the construction phase, based on sustainable BIM (digital continuity, frugality of models) - Developing digital twins (exploring the potential of AI for decision support), using opportunities with regard to biodiversity and the environment - Use the digital twin to improve resilience to climate change - Develop an industrializable, standardized and shared vision of interfaces ensuring digital continuity via the BIM model on all phases - Build a collaborative ecosystem around the modeling of linear and particularly railway infrastructure

The team participates with BIM and monitoring of railway structures by modeling vibrations, defining original ways of operational monitoring including fiber optic sensors.

The city of Rennes has allocated 10k€ to E. Denimal to facilitate her installation and engage collaborations (2021–2023).

The city of Rennes has allocated 10k€ to C. Droz to facilitate his installation and engage collaborations (2022–2024).

The region Pays de la Loire, has allocated 48k€ to R. Noël to his project on numerical simulations of phase change material for thermal regulation of cities (2022–2024).