Etienne Videcoq

Thermal behavior of an electrical motor through a reduced model

The aim of this study is to obtain quickly thermal information on some sensitive components of an electrical motor in a short lapse of time. The thermal behavior of this complex system is modeled and validated. The corresponding detailed model leads to the resolution of a linear system of differential equations of high order, but is not easy to handle for control purposes, due to long CPU time. In order to compute faster, two model reduction techniques are used: the Eitelberg method and the reduction by modal identification. The reduced models effectively give good temperature accuracy on the critical points of the motor with very fast computation time.

Experimental modelling and estimation of time varying thermal sources

Abstract This paper shows an experimental design where two steps are carried out: (i) the identification of a low order state representation through temperature evolutions corresponding to step responses of a system, (ii) the use of this model to solve an inverse heat conduction problem (IHCP) consisting in the estimation of several strength variations generated by heat sources from time-varying temperature evolutions. Experiments are realized on a 3D heat conductive system (a thick stainless steel tube) in which are set four heat sources, a fifth thermal strength consists in an applied flux boundary condition. After the model identification, a sequential method is used for the resolution of the IHCP: from temperature measurements, the evolutions of the five strengths are identified and compared to the electrical measurements.

Comparison of Two Nonlinear Model Reduction Techniques: The Modal Identification Method and the Branch Eigenmodes Reduction Method

This article shows the comparison of two modal reduction techniques, the modal identification method and the branch eigenmodes reduction method. The objective of these methods is to reduce the number of states representing the system evolution in order to decrease the computational time necessary for the simulation. After a presentation of both techniques, a comparison is made on a 3-D nonlinear transient thermal diffusive system. Results given by the two reduced models are compared to those given by the detailed model. The accuracy of both reduced models, as well as the gain in computational time, are analyzed for each configuration.

The Use of Model Reduction and Function Decomposition for Identifying Boundary Conditions of A Linear Thermal System

This numerical study deals with the identification of space and time varying inputs applied to a linear diffusive thermal system. Such an Inverse Heat Conduction Problem (IHCP) is ill-posed, its resolution is difficult for a large amount of unknowns and requires large memory size and computing time for multidimensional cases. Consequently, we propose a procedure to reduce both the number of unknowns and the model order. A 2D example is presented, with a heat flux density φ(y,t) to be identified from simulated transient temperature measurements. Starting from a Classical Detailed Model (CDM), two steps are performed. Firstly, a decomposition of the spatial distribution of φ on a functions basis leads to a small number of unknowns. Secondly, a Reduced Model (RM) is built using the Modal Identification Method. When RM is used to solve the inverse problem instead of CDM, computing time is drastically reduced (up to a factor 1000) whilst preserving accuracy. A procedure to determine the number of unknown coefficients is proposed. The inversion algorithm is sequential and requires no iterations. Future time steps with a function specification are used as a regularisation procedure. Tikhonovs regularisation is needed with CDM but not with RM.

Online Temperature Prediction Using a Branch Eigenmode Reduced Model Applied to Cutting Process

In this article, we propose a method to estimate the temperature field in the hottest zone of a cutting tool. Since temperature measurements are not possible in this zone, an inverse method using a branch modal reduction is implemented. The reduced model is used in an inverse problem to identify the heat flux density generated by the frictional forces. Knowing the interface heat flux, the direct problem is solved to compute the temperature field in the tool. The analysis of the results shows that this method enables supervision of the temperature field at the workpiece-tool contact area in real time.

Parametric low-order models in transient heat diffusion by MIM. Estimation of thermal conductivity in a 2D slab

Classical modeling methods based on spatial discretization of local governing equations lead to fine meshes, resulting in large size models which require huge computing times. In applications such as on-line inverse or real-time feedback control problems, this issue becomes crucial. Several techniques have been developed for building low-order models, involving a smaller set of equations and able to reproduce the thermal behavior of a reference large-size model or an actual system, whatever the time-varying boundary conditions and/or heat source terms, or for a range of values of a thermophysical parameter. But low-order models able to mimic heat transfer dynamics for both a time-varying thermal load and a physical parameter range are not frequently encountered. Such a problem is addressed here, through an extension of the Modal Identification Method. The approach is illustrated on a simple linear 2D transient heat diffusion problem, with a time-varying heat flux density applied on one side and a thermal conductivity in the 15 to 45 W.m−1.K−1 range. The low-order model is used for the estimation of the thermal conductivity from the knowledge of both the applied heat flux and a simulated transient temperature measurement on the opposite side. The approach remains valid for 3D cases in complex geometries involving more independent thermal loads.