Section: New Results

Analysis and control of systems

Optimal vibration damping of large structures

Participant : Dominique Siegert.

This paper deals with the theoretical and experimental analysis of magnetically tuned mass dampers, applied to the vibration damping of large structures of civil engineering interest. Two devices are analysed, for which both the frequency tuning ratio and the damping coefficient can be easily and finely calibrated. They are applied for the damping of the vibrations along two natural modes of a mock-up of a bridge under construction. An original analysis, based on the Maxwell receding image method, is developed for estimating the drag force arising inside the damping devices. It also takes into account self inductance effects, yielding a complex nonlinear dependence of the drag force on the velocity. The analysis highlights the range of velocities for which the drag force can be assumed of viscous type, and shows its dependence on the involved geometrical parameters of the dampers. The model outcomes are then compared to the corresponding experimental calibration curves. A dynamic model of the controlled structure equiped with the two damping devices is presented, and used for the development of original optimization expressions and for determining the corresponding maximum achievable damping. Finally, several experimental results are presented, concerning both the free and harmonically forced vibration damping of the bridge mock-up, and compared to the corresponding theoretical predictions. The experimental results reveal that the maximum theoretical damping performance can be achieved, when both the tuning frequencies and damping coefficients of each device are finely calibrated according to the optimization expressions [15] , [46] .

Particle filtering techniques for monitoring of structures

Participant : Laurent Mevel.

The focus of this paper is Bayesian modal parameter recursive estimation based on an interacting Kalman filter algorithm with decoupled distributions for frequency and damping. Interacting Kalman filter is a combination of two widely used Bayesian estimation methods: the particle filter and the Kalman filter. Some sensitivity analysis techniques are also proposed in order to deduce a recursive estimate of modal parameters from the estimates of the damping/stiffness coefficients [30] .

Uncertainty quantification

Participants : Michael Doehler, Laurent Mevel.

For applications as Operational Modal Analysis (OMA) of vibrating structures, an output-only LTI system with state and measurement noise can be identified using subspace methods. While these identification techniques have been very suitable for the identification of such mechanical, aeronautical or civil structures, covariance expressions of the estimates of the system matrices are difficult to obtain and theoretical results from literature are hard to implement for output-only systems with unknown noise properties in practice. Moreover, the model order of the underlying system is generally unknown and due to noise and model errors, usual statistical criteria cannot be used. Instead, the system is estimated at multiple model orders and some GUI driven stabilization diagram containing the resulting modal parameters is used by the structural engineer. Then, the covariance of the estimates at these different model orders is an important information for the engineer, which, however, would be computationally expensive to obtain with the existing tools. Recently a fast multi-order version of the stochastic subspace identification approach has been proposed, which is based on the use of the QR decomposition of the observability matrix at the largest model order. In this paper, the corresponding covariance expressions for the system matrix estimates at multiple model orders are derived and successfully applied on real vibration data [38] , [40] .

Periodic systems

Participants : Ivan Guéguen, Laurent Mevel.

The modal analysis of a wind turbine has been generally handled with the assumption that this structure can be accurately modeled as linear time-invariant. Such assumption may be misleading for stability analysis, especially, with the current development of very large wind turbines with complex dynamic behavior (nonlinearity, aeroelastic coupling). Therefore in this paper, the inherent periodically time-varying dynamics of wind turbines (and for rotating systems, in general) is taken into account. Recently a subspace algorithm for modal analysis of rotating systems has been proposed. It is tested on a simulated and real data from a wind turbine [22] , [43] .

Identification of finite impulse response systems based on quantized output measurements – a quadratic programming-based method

Participant : Qinghua Zhang.

This work has been carried out in collaboration with Jiandong Wang (Peking University, China).

Quantized data are typically produced by the process of analog-to-digital conversion and have been widely studied in signal encoding and digital representation. In system identification, the processed data are usually collected after a quantization procedure, but the effect of quantization is often ignored. The study on system identification based on quantized data makes sense when the data are coded with few quantization levels, to the point that the effect of quantization becomes important. In this work we propose a quadratic programming (QP)-based method for identification of finite impulse response (FIR) dynamic systems from quantized or binary data. The main idea of the proposed method is to reformulate this identification problem, usually viewed as a nonlinear estimation problem with discontinuous nonlinearities, in the form of a standard QP problem, which is a convex optimization problem and can be solved efficiently. The complete input conditions ensuring the strict convexity of the QP problem are developed, and the consistency of the estimated parameters is established under the complete input conditions. The results of this study have been published in [29] .

Wiener System Identification by Weighted Principal Component Analysis

Participant : Qinghua Zhang.

This work has been carried out in collaboration with Vincent Laurain (CRAN/CNRS/Université de Lorraine).

A Wiener system consists of two subsystems connected in series, with a linear dynamic subsystem preceding a static nonlinearity. In the field of control systems, the dynamics of a nonlinear system can often be linearized around its working point. Nevertheless, if its output sensor is affected by strongly nonlinear distortions, the linearization of the sensor characteristics may induce large modeling errors. In such situations, Wiener system model is more appropriate than fully linearized models. Wiener system identification is investigated in this work with a finite impulse response (FIR) model of the linear subsystem. Under the assumption of Gaussian input distribution, this work mainly aims at addressing a deficiency of the well-known correlation-based method for Wiener system identification: it fails when the nonlinearity of the Wiener system is an even function. This method is, in the considered Gaussian input case, equivalent to the best linear approximation (BLA) method, which exhibits the same deficiency. Our new method is based on a weighted principal component analysis (wPCA). Its consistency is proved for Wiener systems with either even or non even nonlinearities. Its computational cost is almost the same as that of a standard PCA.The results of this study have been presented at [53] .

Industrial process for road buildings

Participant : Jean Dumoulin.

The increasing use of the baffled-rotary kiln equipment in many innovative materials processing industrial applications suggests examining the heat transfer phenomena in order to improve the multi-phase flow modeling tools. Their development and use will be relevant for tackling the current energy issues. The heat transfer models available for the rotary kiln in the literature are, for now, not enough efficient for the baffled-rotary kiln case. The present paper is aimed at suggesting a wall heat transfer correlation for the rotary kilns with the secondary inlet. The experimental thermal data acquired within large-scale rotary drum applied to the asphalt concrete materials production, are remained in order to give rise the new issues. These latter results are connected to a visualization campaign performed at the pilot-scale in order to assess the transversal distribution of the granular phase materials. Their analysis suggests a more appropriate physical modelling of the wall heat transfer path. It leads to transform the classical correlation of type Nu=f(Re,Pr) in a new expression of type Nu=f(Re,St) based on a new physical modeling inventory corresponding to the hot and cold fluxes flowing within the baffled-rotary kiln. Thus, the major modification is based on the introduction of the Stanton (St) number in the wall heat transfer correlation. This expression is found more convenient for the baffled-rotary kiln application. This new expression is validated by the comparison with the experimental Nusselt numbers calculated from the inner heat transfer measurements coefficient measured in the baffled-rotary kiln performed at large scale [23] .

Industrial process for concrete structure reparation

Participant : Jean Dumoulin.

In civil engineering, reinforced concrete repair by CFRP is a strengthening technique that has proven successfully in the past. The present study is aimed at using thermoplastic CFRP sheets applied and glued under heat. In this research framework, active thermography is used to accomplish two roles: control of the operating temperature of the thermoplastic CFRP sheets during the installation process and evaluation of the bonding quality after welding. The pap er presents results obtained in laboratory with a dedicated test bench coupled with numerical simulations of the process [51] .

Building energy management

Participants : Alexandre Nassiopoulos, Jordan Brouns.

Problems such as parameter identification for model calibration, optimal design or optimal energy management can all be formulated in a similar framework as problems consisting in finding the minimum of a cost function. The paper presents the software ReTrofiT that specifically treats this kind of problems applied to building energy performance models. ReTrofiT is first of all a simulation tool for evaluating building thermal behavior and computing energy consumptions. The novelty compared to state-of-the-art energy simulation software is that it also integrates a generic set of tools and algorithms to set up and solve optimization problems related to the building thermal model. The use of the adjoint model, that is intrinsically implemented in the code, constructs fast and efficient algorithms to solve linear, non linear, constrained or unconstrained problems addressing a wide range of applications [45] .