Section: New Results

System identification

Linear parameter varying system local model interpolation

Participant : Qinghua Zhang.

The local approach to linear parameter varying (LPV) system identification consists in interpolating a collection of linear time invariant (LTI) models, which have been estimated from data acquired at different working points of a nonlinear system. Interpolation is essential in this approach. When the local LTI models are in state-space form, as each local model can be estimated with an arbitrary state basis, it is widely acknowledged that the local models should be made coherent before their interpolation. In order to avoid the delicate task of making local state-space models coherent, a new interpolation method of local state-space models is proposed in this work, which does not require coherent local models. This method is based on the reduction of the large state-space model built by combining the local models. This work has been presented at SYSID 2018 [39].

State estimation for stochastic time varying systems with disturbance rejection

Participant : Qinghua Zhang.

State estimation in the presence of unknown disturbances is useful for the design of robust systems in different engineering fields. Most results available on this topic are restricted to linear time invariant (LTI) systems, whereas linear time varying (LTV) systems have been studied to a lesser extent. Existing results on LTV systems are mainly based on the minimization of the state estimation error covariance, ignoring the important issue of the stability of the state estimation error dynamics, which has been a main focus of the studies in the LTI case. The purpose of this work is to propose a numerically efficient algorithm for state estimation with disturbance rejection, in the general framework of LTV stochastic systems, including linear parameter varying (LPV) systems, with easily checkable conditions guaranteeing the stability of the algorithm. The design method is conceptually simple: disturbance is first rejected from the state equation by appropriate output injection, then the Kalman filter is applied to the resulting state-space model after the output injection. This work has been carried out in collaboration with Beijing University of Posts and Telecommunications (China) and has been presented at SYSID 2018 [40].

Variance estimation of modal indicators from subspace-based system identification

Participants : Michael Doehler, Laurent Mevel.

This work has been carried out in collaboration with Szymon Gres at Aalborg University and Palle Andersen at SVS.

One of the other practical modal indicators is Modal Assurance Criterion (MAC), for which uncertainty computation scheme is missing. This paper builds on the previous results using the propagation of the measurement uncertainties to estimates of MAC. The sensitivity of the MAC with respect to output covariances is derived using a first order perturbations and the uncertainties are propagated using the Delta method. The influence of the underlying mode shape scaling on both the uncertainty of mode shapes and MAC is investigated [22].

On damage detection system information for structural systems

On damage detection system information for structural systems

Participant : Michael Doehler.

Damage detection systems (DDSs) provide information on the integrity of structural systems in contrast to local information from inspections or non-destructive testing (NDT) techniques. In this paper, an approach is developed that utilizes DDS information to update structural system reliability and integrate this information into risk and decision analyses. For updating of the structural system reliability, an approach is developed based on Bayesian updating facilitating the use of DDS information on structural system level and thus for a structural system risk analysis. The structural system risk analysis encompasses the static, dynamic, deterioration, reliability and consequence models, which provide the basis for calculating the direct risks due to component failure and the indirect risks due to system failure[16].

The effects of deterioration models on the value of damage detection information

Participant : Michael Doehler.

This paper addresses the effects of the deterioration on the value of damage detection information. The quantification of the value of damage detection information for deteriorated structures is based on Bayesian pre-posterior decision analysis, comprising structural system performance models, consequence, benefit and costs models and damage detection information models throughout the service life of a structural system. With the developed approach, the value of damage detection information for a statically determinate Pratt truss bridge girder subjected to different deterioration models is calculated. The analysis shows the impact of the deterioration model parameters on the value of damage detection information. [28].

The effects of SHM system parameters on the value of damage detection information

Participant : Michael Doehler.

This paper addresses how the value of damage detection information depends on key parameters of the Structural Health Monitoring (SHM) system including number of sensors and sensor locations. The quantification of the value of information (VoI) is an expected utility based Bayesian decision analysis method for quantifying the difference of the expected economic benefits with and without information. The (pre-)posterior probability is computed utilizing the Bayesian updating theorem for all possible indications. Through the analysis of the value of information with different SHM system characteristics, the settings of DDS can be optimized for minimum expected costs and risks before implementation [29].

Filtering approaches for damage detection

Adaptive Kalman filter for actuator fault diagnosis

Participant : Qinghua Zhang.

An adaptive Kalman filter is proposed in this work for actuator fault diagnosis in discrete time stochastic time varying systems. By modeling actuator faults as parameter changes, fault diagnosis is performed through joint state-parameter estimation in the considered stochastic framework. Under the classical uniform complete observability-controllability conditions and a persistent excitation condition, the exponential stability of the proposed adaptive Kalman filter is rigorously analyzed. In addition to the minimum variance property of the combined state and parameter estimation errors, it is shown that the parameter estimation within the proposed adaptive Kalman filter is equivalent to the recursive least squares algorithm formulated for a fictive regression problem. These results have been published in [17].

Zonotopic state estimation and fault detection for systems with both time-varing and time-invariant uncertainties

Participant : Qinghua Zhang.

This paper proposes a robust guaranteed state estimation method with application to fault detection by combining $H_{\infty }$ observer design with zonotopic analysis for discrete-time systems with both time-varing and time-invariant uncertainties. In order to improve the estimation accuracy, based on the $H_{\infty }$ technique, the observer design is achieved by solving a linear matrix inequality. The main contribution of this paper lies in that the time invariance of some uncertainties is considered to reduce the conservatism of interval estimation. This work has been carried out in collaboration with Harbin Institute of Technology (China) and with Universitat Politècnica de Catalunya (Spain), and has been presented at SAFEPROCESS 2018 [37].

Local adaptive observers for time-varying systems with parameter-dependent state matrices

Participant : Qinghua Zhang.

The purpose of this work is to design an adaptive observer for linear time-varying systems whose state matrix is affine in some unknown parameters. In this case, the proposed observer generates state and parameter estimates, which exponentially converge to the plant state and the true parameters, respectively. The results are then extended to systems whose state matrix is nonlinear, instead of being affine, in the unknown parameters. This work has been carried out in collaboration with Université de Lorraine-CNRS-CRAN and has been presented at CDC 2018 [45].

Seismic-induced damage detection through parallel force and parameter estimation using an improved interacting Particle-Kalman filter

Standard filtering techniques for structural parameter estimation assume that the input force is either known or can be replicated using a known white Gaussian model. Unfortunately for structures subjected to seismic excitation, the input time history is unknown and also no previously known representative model is available. In this paper, the input force is considered to be an additional state that is estimated in parallel to the structural parameters. Two concurrent filters are employed for parameters and force respectively. For the parameters, an interacting Particle-Kalman filter is used to target systems with correlated noise. Alongside this, a second filter is used to estimate the seismic force acting on the structure [15].

Bayesian parameter estimation for parameter varying systems using interacting Kalman filters

Participants : Antoine Crinière, Laurent Mevel, Jean Dumoulin.

Existing filtering based structural health monitoring (SHM) algorithms assume constant noise environment which does not always conform to the reality as noise is hardly stationary. Thus to ensure optimal solution even with non-stationary noise processes, the assumed statistical noise models have to be updated periodically. This work incorporates a modification in the existing Interacting Particle-Kalman Filter (IPKF) to enhance its detection capability in presence of non-stationary noise processes. The Kalman filters (KF) within the IPKF have been replaced with a maximum Correntropy criterion (MCC) based KF that, unlike regular KF, takes moments beyond second order into consideration [32].

Damage localization for mechanical structures

Damage localization using the stochastic load vectors

Participants : Laurent Mevel, Michael Doehler.

This work was done in collaboration with BAM (Berlin) and GEM (Nantes).

In this work, a benchmark application is proposed, namely a 1/200 scale model of the Saint-Nazaire Bridge, which is a cable-stayed bridge spanning the Loire River near the river's mouth. The region of interest, the central metallic structure, measures 720 meters. The aim of the instrumentation is to assess the capability of damage assessment methods to assess a cable failure. The model is instrumented with ten accelerometers and excited by white noise. A damage localization method is applied to test the proposed setup, namely the statistical damage locating vector approach (S-SDDLV). With this method, vibration measurements from the (healthy) reference and damaged states of the structure are confronted to a finite element of the reference state. Damage indicators are provided for the different structural elements that are easy to compute, without updating the model parameters, and taking into account the intrinsic uncertainty of noisy measurements. [21].

Asymptotic analysis of subspace-based data-driven residual for fault detection with uncertain reference

Participants : Laurent Mevel, Michael Doehler, Eva Viefhues.

This work was in collaboration with BAM (Berlin).

The local asymptotic approach is promising for vibration-based fault diagnosis when associated to a subspace-based residual function and efficient hypothesis testing tools. In the residual function, the left null space of the observability matrix associated to a reference model is confronted to the Hankel matrix of output covariances estimated from test data. When this left null space is not perfectly known from a model, it should be replaced by an estimate from data to avoid model errors in the residual computation. In this paper, the asymptotic distribution of the resulting data-driven residual is analyzed and its covariance is estimated, which includes also the covariance related to the reference null space estimate [36].

Smarts roads and R5G

Multi-physics models for Energy Harvesting performance evaluation

Participants : Jean Dumoulin, Nicolas Le Touz.

We present in this paper the concept of solar hybrid road and focus on the thermal performances of such system. A finite element model is presented to couple thermal diffusion, hydraulic convection and radiative transfer. This numerical model allows to compute the temperature field for different weather conditions and also to evaluate the thermal performances of the system. Annual simulations are performed and a comparison between two surface layer solutions for different locations and climates is presented and discussed[23].

Optimal command for defreezing of solar road

Participants : Jean Dumoulin, Nicolas Le Touz.

The study presented in [26] aims to optimize the amount of energy to bring to a hybrid solar road to prevent the formation of ice on the surface. The optimal control law studied is based on a finite element multiphysics model, developed to compute the temperature field in the structure under varying environmental conditions presented in [25]. A penalization of freezing periods at the surface is introduced and the energy to be supplied to the system to preserve it is calculated from the adjoint state method [24].

Infrared Thermography

Sensitivity of infrared camera to environmental parameters

Participants : Laurent Mevel, Jean Dumoulin, Thibaud Toullier.

The purpose of this study is to characterize the influence of environmental parameters for long-term in-situ structure monitoring as well as projections errors due to camera view and digitization. The model used to convert 3 year gathered data to temperature is firstly presented and discussed. Then, the effect of camera resectioning on infrared measurements is commented. Finally, the effect of the environmental parameters is studied and perspectives are proposed [35].

Joint Estimation of emissivity and temeperature

Participants : Laurent Mevel, Jean Dumoulin, Thibaud Toullier.

This study deals with the simultaneous assessment of emissivity and surface temperature. of objects observed by in-situ infrared thermography. Temperature measurement by thermography infrared is hampered by the lack of knowledge of the radiative properties of the real world. The light received from a target by an infrared camera is estimated by the method of progressive radiosities implemented on a map graphic in order evaluate the sensitivity of four methods of separation of emissivity and temperature [34].

Sensor and hardware based research

Reflectometry

Participant : Qinghua Zhang.

De-embedding unmatched connectors for electric cable fault diagnosis

Participant : Qinghua Zhang.

In order to make accurate reflectometry measurements on electric cables for fault diagnosis, connector de-embedding is a procedure for compensating measurement distortions caused by unmatched connectors. The key step in such a procedure is the characterization of the connectors, which is realized through measurements on a pair of connectors linked by a short cable segment. The analysis for deducing the characteristics of a single connector from measurements made on an assembled pair is known as the bisection problem. In this paper, after recalling the underdetermined nature of the bisection problem, a practically effective de-embedding procedure is proposed based on a particular regularization technique. This work has been carried out in collaboration with EDF R&D and has been presented at SAFEPROCESS 2018 [38].

Active Infrared thermography by robot

Participants : Jean Dumoulin, Ludovic Gaverina.

In this paper, two Non Destructive Testing approaches by active infrared thermography mounted on a 6-axis robot are presented and studied. An automated procedure is proposed to reconstruct thermal image sequences issued from the two scanning procedure studied: Line Scan and Flying Line procedures. Defective area detection is performed by image processing and an inverse technique based on thermal quadrupole method is used to map the depth of flaws [31].

Shunting monitoring in railway track circuit receivers

Participant : Vincent Le Cam.

Track circuits play a major role in railway signaling. In some exceptional conditions, poor rail/wheel contact conditions may lead to a non-detection of the train on the zone. The paper presents new detection approaches based on signal processing on an experiment with a dedicated train running on a track equipped with a track circuit. The second objective is to present a strategy to test new detection criteria on commercial zones over a long period of time using PEGASE [30].