Yves Candau

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.

A simultaneous characterization of thermal conductivity and diffusivity of polymer materials by a periodic method

A periodic method is used to determine simultaneously both thermal conductivity and diffusivity of various polymer materials at room temperature. The sample is placed between two metallic plates and temperature modulation is applied on the front side of one of the metallic plates. The temperature at the front and rear sides of both plates is measured and the experimental transfer function is calculated. The theoretical thermal heat transfer function is calculated by the quadrupole method. Thermal conductivity and diffusivity are simultaneously identified from both real and imaginary parts of the experimental transfer function. The thermophysical parameters of several polymer samples (PTFE, PVDF and PA11) with different thicknesses (respectively, 5 mm, 2 mm and 300 µm) were studied and compared with values from the literature. The values identified for the thermal parameters are in good agreement with values from the literature for PTFE and PVDF samples; however, we show that the method reaches its limit for the thinner PA11 sample, owing to inadequacy of the thermal model.

A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems

In this paper, we show how to compute an over-approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on state-of-the-art validated numerical integration methods. The second one relies on comparison theorems for differential inequalities in order to bracket the uncertain dynamics between two dynamical systems where there is no uncertainty. Since the derived bracketing systems are piecewise Ck-differentiable functions, validated numerical integration methods cannot be used directly. Hence, our contribution resides in the use of hybrid automata to model the bounding systems. We give a rule for building these automata and we show how to run them and address mode switching in a guaranteed way in order to compute the over approximation for the reachable set. The computational cost of our method is also analyzed and shown to be smaller that the one of classical interval techniques. Sufficient conditions are given which ensure the epsiv-practical stability of the enclosures given by our hybrid bounding method. Two examples are also given which show that the performance of our method is very promising.

Infrared emissivity measurement device : principle and applications

Infrared emissivity is a necessary parameter for computing models to predict road surface status and pavement temperature irrespective of the weather situation. In this work a new experimental device based on the indirect method was developed for the measurement of surface emissivities. The surface is exposed to modulated isotropic infrared radiation. The intensity reflected by the surface of the sample in a given direction is measured by a detector operating in the spectral range 1–40 µm. This large spectral range allows measurement of the total hemispheric emissivity defined in this case as emissivity. The effect of the temperature modulation frequency, surface composition and surface roughness on the emissivity measurements was investigated. The results show good ability of the device for the determination of emissivities at room temperature.

Reachability of Uncertain Nonlinear Systems Using a Nonlinear Hybridization

In this paper, we investigate nonlinear reachability computation in presence of model uncertainty, via guaranteed set integration. We show how this can be done by using the classical Mullers existence theorem. The core idea developed is to no longer deal with whole sets but to derive instead two nonlinear dynamical systems which involve no model uncertainty and which bracket in a guaranteed way the space reachable by the original uncertain system. We give a rule for building the bracketing systems. In the general case, the bracketing systems obtained are only piecewise Ck-continuously differential nonlinear systems and hence can naturally be modeled with hybrid automata. We show how to derive the hybrid model and how to address mode switching. An example is given with a biological process.

Complex Interval Arithmetic Using Polar Form

In this paper, the polar representation of complex numbers is extended to complex polar intervals or sectors; detailed algorithms are derived for performing basic arithmetic operations on sectors. While multiplication and division are exactly defined, addition and subtraction are not, and we seek to minimize the pessimism introduced by these operations. Addition is studied as an optimization problem which is analytically solved. The complex interval arithmetic thus defined is illustrated with some numerical examples which show that in many applications, the polar representation is more advisable.

Analysis of uncertainties in thermophysical parameters of materials obtained from a periodic method

In the present work, we are interested in the improvement and the validation of the identification procedure for the simultaneous estimation of thermophysical parameters and their uncertainties using a periodic method. The effect of the statistical uncertainties on the estimation procedure and the reproducibility study of experimental device and measurement method are presented. In addition, the effect of the uncertainties of supposedly known model parameters on the identification procedure was investigated. The results show good reproducibility of the experimental results, and the uncertainty related to reproducibility is negligible. However, conductivity and diffusivity of the copper plate, and heat coefficient exchange, are parameters that strongly affect the result of the identification procedure.

Experimental investigation of a composite phase change material: Thermal-energy storage and release

In recent times, composites made out of polymers and paraffin waxes were thought to be good thermal energy storage materials, in which the heat is stored as latent heat of fusion in the paraffin wax. In this study, phase change composite material with spherical shape calibrated based paraffin wax (RT27) was produced. The properties of the prepared composite phase change material have been characterized. The objective of this article was to study the energy storage and the energy recovery by using a phase change composite material. An experimental set-up consisting of fluxmetric measurement has been constructed to provide the thermal performance of the composite. In addition, a differential scanning calorimetry analysis was carried out. The experimental apparatus allows providing heat storage capacities and “apparent” thermal conductivities of the composite at the solid and liquid states, and also a measurement of the latent heat of fusion. The proposed test provides temperature and heat flux measurements at the material borders. The amount of energy exchanged during the variation of the thermodynamic state samples could be calculated when the boundary temperatures vary. In this article, one shows how it can allow the study of complex composite material with PCM. In particular, heat flux measurements make it possible to highlight very specific behaviors of these products and are thus a very interesting experimental source of data which comes to complete the traditional measurement methods like calorimetric device (differential scanning calorimetry).

Thermal and mechanical properties of maize fibres–high density polyethylene biocomposites:

In recent years, considerable attention has been given to the development and utilization of natural fibres. This study examines the thermal properties of maize thermomechanical fibre reinforced high density polyethylene composites with competitive mechanical properties. The composites were produced by six different steps, namely: drying, cutting, mixing, compounding, pelletizing and injection moulding. Composite samples with fibre contents in the range 10–40 wt% were chosen to observe their effect on thermal and mechanical properties as the fibre content was increased. Measurements of thermophysical properties were obtained using periodic temperature ramp method. The material characterization was performed on a temperature range that extends from −20℃ to 120℃. It was found that the thermal conductivity and diffusivity of the composites decrease with fibre loading. The results showed that when the temperature is increased, a significant increase of both thermal effusivity and the factor ( ρ c Cp c ) was observed. A high-quality dispersion and adhesion of maize fibre in the high density polyethylene matrix was indicated by scanning electron microscopy. Good mechanical performance of the obtained composites was established considering the stress transfer at fibre–matrix interface.

A comparative analysis of dielectric, rheological and thermophysical behaviour of ethylene vinyl acetate/BaTiO3 composites

Dielectric, rheological and thermal behaviours of ethylene vinyl acetate/barium titanate sphere (EVA/BaTiO3) composite materials were investigated in this work. Several composites were prepared for different volume concentrations (from 5% to 49%) and for two types of spheres sizes d: d = 9 µm and d = 105 µm. We show that the use of larger particles allows an increase of dielectric permittivity and thermal conductivity, particularly at high filler concentrations. A comparison between the thermal, dielectric and rheological behaviours of the composites is also reported in this paper. A linear dependence of the relative variation of thermal conductivity and dielectric permittivity, on the one hand, and thermal conductivity and Newtonian viscosity, on the other, was shown.