Frédéric Bourquin

A magnet-based vibrating wire sensor: design and simulation

Vibrating strings help in measuring relative displacements in a mechanical system. Since the ground natural frequency of a string increases when it is stretched, monitoring the ground frequency yields the current length of the string. Therefore a wire able to vibrate between two anchor points of a system acts as a relative displacement sensor. Excitation is usually achieved by means of an active coil, which is very close to the vibrating iron wire. Vibrating wire sensors (VWS) based on this excitation may prove obtrusive and one is limited to wires of small length. The new VWS takes advantage of distributed passive magnets, which force the wire to vibrate mainly in its fundamental mode. The sensor proves scalable and much less obtrusive when fully embedded, since it can be made flat and very flexible. On the basis of a simplified electromechanical modelling of the measurement process, a suitable distribution of magnets is proposed, which is proved numerically and experimentally to make the measurement robust with respect to mechanical uncertainties. Moreover, numerical simulations suggest measuring not the voltage in the vibrating wire but the current in an auxiliary circuit.

On-site building walls characterization

The on-site assessment of dynamic properties of building envelopes is often necessary for accurate analysis of building performance. The main difficulty is that the experiment has to be carried out with unknown thermal loadings on the wall under test. We present a methodology able to address this difficulty: it consists in identifying all-at-once both the sought parameters; i.e., the heat conductivity and capacity, and the unknown thermal loadings. They are obtained as solutions of an inverse problem using only standard temperature measurements as input data. The numerical performance of the methodology, applied to homogeneous walls, is assessed.

Magnetically tuned mass dampers for optimal vibration damping of large structures

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 equipped 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.

Inverse Computational Fluid Dynamics: Influence of Discretization and Model Errors on Flows in Water Network Including Junctions

We present a specific inverse technique to reconstruct water pipe flows from sensor outputs. The spatial shape of the boundary velocities are chosen according to spatial velocity profiles in water pipes that conform the engineering literature. Only the time evolution of the boundary velocity has to be determined using the inverse technique. Thus, few sensors are required to reconstruct a two- or three-dimensional water pipes flow. The methodology is illustrated for three flow models: Stokes, unsteady Stokes and Navier-Stokes. To reduce the computation cost of the reconstruction, simple flow models and coarse discretisations may be employed. Nevertheless this leads to less accurate results. The present paper evaluates the influence of the flow modelling and of the dicretisation on the quality of the reconstructed velocity on two examples: a water pipe junction and a 200 m subsection from a French water network. In the water pipe junction at a 100 Reynolds number, we show that a hybrid approach combining an unsteady Stokes reconstruction and a single direct Navier-Stokes simulation outperforms the algorithms based on a single model. In the network subsection we obtain an L2 error less than 1% between the reference velocity based on Navier-Stokes equations (100 Reynolds number) and the velocity reconstructed from Stokes equation. In this case, the reconstruction lasts less than one minute. Essentially Stokes based reconstruction of a Navier-Stokes flow in junctions at Reynolds number up to 100 yields the same accuracy and proves fast.

Impacts of Discretization Error, Flow Modeling Error, and Measurement Noise on Inverse Transport-Diffusion-Reaction in a T-Junction

By combining a physical model and sensor outputs in an inverse transport-diffusion-reaction strategy, an accurate cartography of the concentration field may be obtained. The paper addresses the influence of discretization errors, flow uncertainties and measurement noise on the reconstruction process of the concentration field. We consider a key element of a drinking water network that is a pipe junction where Reynolds and Peclet numbers are approximately 2000 and 1000 respectively. We show that a 10% error between the reference concentration field and the reconstructed concentration field may be obtained using a coarse discretization. Nevertheless, to keep the error below 10%, a fine concentration discretization is required. The study also details the influence of the flow approximation on the concentration reconstruction process. The flow modeling error obtained when the exact Navier-Stokes flow is approximated by a Stokes flow may lead to a 40% error in the reconstructed concentration. However if the flow field is obtained from the full set of Navier-Stokes equations, we show that the error may be less than 5%. Then, we observe that the quality of the reconstructed concentration field obtained with the proposed inverse technique is not deteriorated when sensor outputs have a normal distribution noise variance of few percents. Lastly, a good engineering practice would be to stop the reconstruction process according to an extended discrepancy principle including modeling and measurement errors. As shown in the article, the quality of the reconstructed field declines after reaching the threshold of the modeling error.

A vectorial descent stepsize for parameter identification of a coupled parabolic PDE-ODE

We consider a simplified model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identification procedure able to reconstruct the parameters of the model. The response of the model is nonlinear with respect to its parameters and the reconstruction of the parameters is achieved by the introduction of a new vectorial descent stepsize, which improves the convergence of the Levenberg–Marquardt minimization algorithm. The new vectorial descent stepsize can have negative and positive entries of different sizes, which fundamentally differs from standard scalar descent stepsize. The new algorithm is proved to converge and to outperform the standard scalar descent strategy. We also propose algorithms for the initialization of the parameters needed by the reconstruction procedure, when no a priori knowledge is available.

Elastodynamics model updating for the monitoring of reinforced concrete beam: methodology and numerical implementation

Reinforced concrete beams are widely employed in civil engineering structures. To reduce the maintenance financial cost, structure damages have to be detected early. To this end, one needs robust monitoring techniques. The paper deals with the identification of mechanical parameters, useful for Structural Health Monitoring, in a 2D beam using inverse modeling technique. The optimal control theory is employed. As an example, we aim to identify a reduction of the steel bar cross-section and a decrease of the concrete Young modulus in damaged areas. In our strategy, the beam is instrumented with strain sensors, and a known dynamic load is applied. In the inverse technique, two space discretizations are considered: a fine dicretization (h) to solve the structural dynamic problem and a coarse discretization (H) for the beam parameter identification. To get the beam parameters, we minimize a classical data misfit functional using a gradient-like algorithm. A low-cost computation of the functional gradient is performed using the adjoint equation. The inverse problem is solved in a general way using engineer numerical tools: Python scripts and the free finite element software Code_Aster. First results show that a local reduction of the steel bar cross-section and a local decrease of concrete Young modulus can be detected using this inverse technique.

Capacitive ultrasonic micro-transducer made of carbon nanotubes: Prospects for the in-situ embedded non-destructive testing of durability in cementitious materials

ABSTRACT We put forward an innovative method for the non-destructive testing of durability in cementitious material. It is based on microporosity probing by high-frequency ultrasonic micro-transducers. We present elements of the realisation and the characterization of such challenging devices. Their design relies on the exceptional mechanical performances of carbon nanotubes. Modelling of the devices in a fluid environment provides a preliminary validation of their suitability for durability monitoring.

IDENTIFICATION OF REINFORCED CONCRETE BEAM PARAMETERS USING INVERSE MODELING TECHNIQUE AND MEASURED DYNAMIC RESPONSES FOR STRUCTURAL HEALTH MONITORING

Reinforced and prestressed concrete beams are widely employed in civil engineering structures, e.g. in simply supported spans using prestressed concrete beams (VIPP). To reduce the financial cost due to maintenance, structure damages have to be detected early. To achieve this purpose, one needs robust monitoring techniques. The paper deals with the determination of mechanical parameters, useful for Structure Health Monitoring, in a 2D beam using inverse modeling technique. The optimal control theory is employed. As an example, we aim to identify a reduction of the steel bar cross-section and a decrease of the concrete Young modulus in damaged area. In our strategy, the beam is instrumented with strain sensors, and a known dynamic load is applied. In the inverse technique, two space discretizations are considered: a fine dicretization (h) to solve the structural dynamic problem and a coarse discretization (H) for the beam parameter identification. To get the beam parameters, we minimize a classical data misfit functional using a gradient-like algorithm. A low-cost computation of the functional gradient is performed using the adjoint problem solution. The inverse problem is solved in a general way using engineer numerical tools: Python scripts and the free finite element software Code Aster. First results show that a local reduction of the steel bar cross-sections and a local decrease of concrete Young modulus can be detected using this inverse technique.

Unimodal optimal passive electromechanical damping of elastic structures

In this paper, a new electromechanical damper is presented and used, made of a pendulum oscillating around an alternator axis and connected by a gear to the vibrating structure. In this way, the mechanical energy of the oscillating mass can be transformed into electrical energy to be dissipated when the alternator is branched on a resistor. This damping device is intrinsically non-linear, and the problem of the optimal parameters and of the best placement of this damper on the structure is studied. The optimality criterion chosen here is the maximum exponential time decay rate (ETDR) of the structural response. This criterion leads to new design formulas. The case of a bridge under construction is considered and the analytical results are compared with experimental ones, obtained on a mock-up made of a vertical tower connected to a free-end horizontal beam, to simulate the behavior of a cable-stayed bridge during the erection phase. Up to three electromechanical dampers are placed in order to study the multi-modal damping. The satisfactory agreement between the theoretical model and the experiments suggests that a multi-modal passive damping of electromagnetic type could be effective on lightweight flexible structures, when dampers are suitably placed.